Tesis sobre el tema "Splitting scheme"

Material point method (MPM) is a numerical tool which was originally used for modelling large deformations of solid mechanics problems. Due to the particle based spatial discretiza- tion, MPM is naturally capable of handling large mass movements together with topological changes. Further, the Lagrangian particles in MPM allow an easy implementation of history dependent materials. So far, however, research on MPM has been mostly restricted to explicit dynamic formu- lations with linear approximation functions. This is because of the simplicity and the low computational cost of such explicit algorithms. Particularly in MPM analysis of geomechan- ics problems, a considerable attention is given to the standard explicit formulation to model dynamic large deformations of geomaterials. Nonetheless, several limitations exist. In the limit of incompressibility, a significantly small time step is required to ensure the stability of the explicit formulation. Time step size restriction is also present in low permeability cases in porous media analysis. Spurious pressure oscillations are another numerical instability present in nearly incompressible flow behaviours. This research considers an implicit treatment of the pressure in MPM algorithm to simu- late material incompressibility. The coupled velocity (v)-pressure (p) governing equations are solved by applying Chorin’s projection method which exhibits an inherent pressure stability. Hence, linear finite elements can be used in the MPM solver. The main purpose of this new MPM formulation is to mitigate artificial pressure oscillations and time step restrictions present in the explicit MPM approach. First, a single phase MPM solver is applied to free surface incompressible fluid flow problems. Numerical results show a better approximation of the pressure field compared to the results obtained from the explicit MPM. The proposed formulation is then extended to model fully saturated porous materials with incompress- ible constituents. A solid velocity(v S )-fluid velocity (v F )-pore pressure (p) formulation is presented within the framework of mixture theory. Comparing the numerical results for the one-dimensional consolidation problem shows that the proposed incompressible MPM algorithm provides a stable and accurate pore pressure field even without implementing damping in the solver. Finally, the coupled MPM is used to solve a two-dimensional wave propagation problem and a plain strain consolidation problem. One of the important features of the proposed hydro mechanical coupled MPM formulation is that the time step size is not dependent on the incompressibility and the permeability of the porous medium.

The present work deals with the extension of Acoustic Flux Vector Splitting (AFVS) scheme for the Compressible Viscous flow computations. Accurate viscous flow computations require much finer grids with adequate clustering of grid points in certain regions. Viscous flow computations are performed on unstructured triangulated grids. Solving Navier-Stokes equations involves the inviscid Euler part and the viscous part. The inviscid part of the fluxes are computed using the Acoustic Flux Vector Splitting scheme and the viscous part which is diffusive in nature does not require upwinding and is taken care using a central difference type of scheme. For these computations both the cell centered and the cell vertex finite volume methods are used. Higher order accuracy on unstructured meshes is achieved using the reconstruction procedure. Test cases are chosen in such a way that the performance of the scheme can be evaluated for different range of mach numbers. We demonstrate that higher order AFVS scheme in conjunction with a suitable grid adaptation strategy produce results that compare well with other well known schemes and the experimental data. An assessment of the relative performance of the AFVS scheme with the Roe scheme is also presented.

The present work deals with the extension of Acoustic Flux Vector Splitting (AFVS) scheme for the Compressible Viscous flow computations. Accurate viscous flow computations require much finer grids with adequate clustering of grid points in certain regions. Viscous flow computations are performed on unstructured triangulated grids. Solving Navier-Stokes equations involves the inviscid Euler part and the viscous part. The inviscid part of the fluxes are computed using the Acoustic Flux Vector Splitting scheme and the viscous part which is diffusive in nature does not require upwinding and is taken care using a central difference type of scheme. For these computations both the cell centered and the cell vertex finite volume methods are used. Higher order accuracy on unstructured meshes is achieved using the reconstruction procedure. Test cases are chosen in such a way that the performance of the scheme can be evaluated for different range of mach numbers. We demonstrate that higher order AFVS scheme in conjunction with a suitable grid adaptation strategy produce results that compare well with other well known schemes and the experimental data. An assessment of the relative performance of the AFVS scheme with the Roe scheme is also presented.

A multi-dimensional upwind fluctuation splitting scheme is developed and implemented for two-dimensional and axisymmetric formulations of the Navier-Stokes equations on unstructured meshes. Key features of the scheme are the compact stencil, full upwinding, and non-linear discretization which allow for second-order accuracy with enforced positivity. Throughout, the fluctuation splitting scheme is compared to a current state-of-the-art finite volume approach, a second-order, dual mesh upwind flux difference splitting scheme (DMFDSFV), and is shown to produce more accurate results using fewer computer resources for a wide range of test cases. The scalar test cases include advected shear, circular advection, non-linear advection with coalescing shock and expansion fans, and advection-diffusion. For all scalar cases the fluctuation splitting scheme is more accurate, and the primary mechanism for the improved fluctuation splitting performance is shown to be the reduced production of artificial dissipation relative to DMFDSFV. The most significant scalar result is for combined advection-diffusion, where the present fluctuation splitting scheme is able to resolve the physical dissipation from the artificial dissipation on a much coarser mesh than DMFDSFV is able to, allowing order-of-magnitude reductions in solution time. Among the inviscid test cases the converging supersonic streams problem is notable in that the fluctuation splitting scheme exhibits superconvergent third-order spatial accuracy. For the inviscid cases of a supersonic diamond airfoil, supersonic slender cone, and incompressible circular bump the fluctuation splitting drag coefficient errors are typically half the DMFDSFV drag errors. However, for the incompressible inviscid sphere the fluctuation splitting drag error is larger than for DMFDSFV. A Blasius flat plate viscous validation case reveals a more accurate vertical-velocity profile for fluctuation splitting, and the reduced artificial dissipation production is shown relative to DMFDSFV. Remarkably the fluctuation splitting scheme shows grid converged skin friction coefficients with only five points in the boundary layer for this case. A viscous Mach 17.6 (perfect gas) cylinder case demonstrates solution monotonicity and heat transfer capability with the fluctuation splitting scheme. While fluctuation splitting is recommended over DMFDSFV, the difference in performance between the schemes is not so great as to obsolete DMFDSFV. The second half of the dissertation develops a local, compact, anisotropic unstructured mesh adaption scheme in conjunction with the multi-dimensional upwind solver, exhibiting a characteristic alignment behavior for scalar problems. This alignment behavior stands in contrast to the curvature clustering nature of the local, anisotropic unstructured adaption strategy based upon a posteriori error estimation that is used for comparison. The characteristic alignment is most pronounced for linear advection, with reduced improvement seen for the more complex non-linear advection and advection-diffusion cases. The adaption strategy is extended to the two-dimensional and axisymmetric Navier-Stokes equations of motion through the concept of fluctuation minimization. The system test case for the adaption strategy is a sting mounted capsule at Mach-10 wind tunnel conditions, considered in both two-dimensional and axisymmetric configurations. For this complex flowfield the adaption results are disappointing since feature alignment does not emerge from the local operations. Aggressive adaption is shown to result in a loss of robustness for the solver, particularly in the bow shock/stagnation point interaction region. Reducing the adaption strength maintains solution robustness but fails to produce significant improvement in the surface heat transfer predictions.
Ph. D.

Analysis of unsteady flows is a very challenging topic of research. A decade ago, potential flow equations were used to predict unsteady pressures on oscillating bodies. Recognising the fact that nonlinear aerodynamics is essential to analyse unsteady flows accurately, particularly in transonic and supersonic flows, different Euler formulations operating on moving grids have emerged recently as important CFD tools for unsteady aerodynamics. Numerical solution of Euler equations on moving grids based on upwind schemes such as the ones due to van Leer and Roe have been developed for the purpose of numerical simulation of unsteady transonic and supersonic flows. In the present work, Euler computations based on yet another recent robust upwind scheme (for steady flows) namely Kinetic Flux Vector Splitting (KFVS) scheme due to Deshpande and Mandal is chosen for further development of a time accurate Euler solver to operate on problems involving moving boundaries. The development of an Euler code based on this scheme is likely to be highly useful to analyse problems of unsteady aerodynamics and computational aeroelasiticity especially when it is noted that KFVS has been found to be an extremely robust scheme for computation of subsonic, transonic, supersonic and hypersonic flows. The KFVS scheme, basically exploits the connection between the linear scalar Boltzmann equation of kinetic theory of gases and the nonlinear vector conservation law, that is, Euler equations of fluid dynamics through moment method strategy. The KFVS scheme has inherent simplicity in splitting the flux even on moving grids due to underlying particle model. The inherent simplicity of KFVS for moving grid problems is due to its relationship with the Boltzmann equation. If a surface is moving with velocity w and a particle has velocity v, then it is quite reasonable to do the splitting based on (v-w)<0 or >0. Only particles having velocity v greater than w will cross the moving surface from left to right and similar arguments hold good for particles moving in opposite direction. It is therefore quite natural to extend KFVS by splitting the Maxwellian velocity distribution at Boltzmann level based on the sign of the normal component of the relative velocity. The relative velocity is the difference between the molecular velocity (v) and the velocity of the moving surface(w). This inherent simplicity of the Kinetic Flux Vector Splitting scheme on Moving Grids (KFMG) method has prompted us to extend the same ideas to 2-D and 3-D problems leading to the present KFMG method. If w is set to zero then KFMG formulation reduces to the one corresponding to KFVS. Thus KFMG formulations axe generalisation of the KFVS formulation. In 2-D and 3-D cases, in addition to the KFMG formulation, the method to move the grids, the appropriate boundary conditions for treating moving surfaces and techniques to improve accuracy in space and time are required to be developed. The 2-D and 3-D formulations based on Kinetic Flux Vector Splitting scheme on Moving Grids method have been developed for computing unsteady flows. Between two successive time steps, the body changes its orientation in case of an oscillation or it deforms when subjected to, aerodynamic loads. In either of these cases the grid corresponding to the first time step has to be moved or regenerated around the displaced or deformed body. There are several approaches available to generate grids around moving bodies. In the present work, the 'spring analogy method' is followed to obtain grid around deflected geometries within the frame work of structured grid. Using this method, the grids are moved from previous time to the current time. This method is capable of tackling any kind of aeroelastic deformation of the body. For oscillating bodies, a suitable boundary condition enforcing the flow tangency on the body needs to be developed. As a first attempt, the body surface has been treated as an 1-D piston undergoing compression and expansion. Then, a more general Kinetic Moving Boundary Condition(KMBC) has been developed. The KMBC uses specular reflection model of kinetic theory of gases. In order to treat fixed outer boundary, Kinetic Outer Boundary Condition(KOBC) has been applied. The KOBC is more general in the sense that, it can treat different type of boundaries (subsonic, supersonic, inflow or out flow boundary). A 2-D cell-centered finite volume KFMG Euler code to operate on structured grid has been developed. The time accuracy is achieved by incorporating a fourth order Runge-Kutta time marching method. The space accuracy has been enhanced by using high resolution scheme as well as second order scheme using the method of reconstruction of fluxes. First, the KFMG Euler code has been applied to standard test cases for computing steady flows around NACA 0012 and NACA 64AQ06 airfoils in transonic flow. For these two airfoils both computational and experimental results are available in literature. It is thus possible to verify (that is, prove the claim that code is indeed solving the partial differential equations + boundary conditions posed to the code) and validate(that is, comparison with experimental results) the 2-D KFMG Euler code. Having verified and validated the 2-D KFMG Euler code for the standard test cases, the code is then applied to predict unsteady flows around sinusoidally oscillating NACA 0012 and NACA 64A006 airfoils in transonic flow. The computational and experimental unsteady results are available in literature for these airfoils for verification and validation of the present results. The unsteady lift and normal force coefficients have been predicted fairly accurately by all the CFD codes. However there is some difficulty about accurate prediction of unsteady pitching moment coefficient. Even Navier-Stokes code could not predict pitching moment accurately. This issue needs further in depth study and probably intensive computation which have not been undertaken in the present study. Next, a two degrees of £reedom(2-DOF) structural dynamics model of an airfoil undergoing pitch and plunge motions has been coupled with the 2-D KFMG Euler code for numerical simulation of aeroelastic problems. This aeroelastic analysis code is applied to NACA 64A006 airfoil undergoing pitch and plunge motions in transonic flow to obtain aeroelastic response characteristics for a set of structural parameters. For this test case also computed results are available in literature for verification. The response characteristics obtained have showed three modes namely stable, neutrally stable and unstable modes of oscillations. It is interesting to compare the value of airfoil-to-air mass ratio (Formula) obtained by us for neutrally stable condition with similar values obtained by others and some differences between them are worth mentioning here. The values of \i for neutral stability are different for different authors. The differences in values of (Formula) predicted by various authors are primarily due to differences which can be due to grid as well as mathematical model used. For example, the Euler calculations, TSP calculations and full potential calculations always show differences in shock location for the same flow problem. Changes in shock location will cause change in pressure distribution on airfoil which in turn will cause changes in values of \L for conditions of neutral stability. The flutter speed parameter(U*) has also been plotted with free stream Mach number for two different values of airfoil - to - air mass ratio. These curves shown a dip when the free stream Mach number is close to 0.855. This is referred as "Transonic Dip Phenomenon". The shock waves play a dominant role in the mechanism of transonic dip phenomenon. Lastly, cell-centered finite volume KFMG 3-D Euler code has been developed to operate on structured grids. The time accuracy is achieved by incorporating a fourth order Runge-Kutta method. The space accuracy has been enhanced by using high resolution scheme. This code has 3-D grid movement module which is based on spring analogy method. The KMBC to treat oscillating 3-D configuration and KOBC for treating 3-D outer boundary have also been formulated and implemented in the code. The 3-D KFMG Euler code has been first verified and validated for 3-D steady flows around standard shapes such as, transonic flow past a hemisphere cylinder and ONERA M6 wing. This code has also been used for predicting hypersonic flow past blunt cone-eylinder-flare configuration for which experimental data are available. Also, for this case, the results are compared with a similar Euler code. Then the KFMG Euler code has been used for predicting steady flow around ogive-cylinder-ogive configuration with elliptical cross section. The aerodynamic coefficients obtained have been compared with those of another Euler code. Thus, the 3-D KFMG Euler code has been verified and validated extensively for steady flow problems. Finally, the 3-D KFMG based Euler code has been applied to an oscillating ogive-cylinder-ogive configuration in transonic flow. This test case has been chosen as it resembles the core body of a flight vehicle configuration of interest to DRDO,India. For this test case, the unsteady lift coefficients are available in literature for verifying the present results. Two grid sizes are used to perform the unsteady calculations using the present KFMG 3-D Euler code. The hysteresis loops of lift and moment coefficients confirmed the unsteady behaviour during the oscillation of the configuration. This has proved that, the 3-D formulations are capable of predicting the unsteady flows satisfactorily. The unsteady results obtained for a grid with size of 45x41x51 which is very close to the grid size chosen in the reference(Nixon et al.) are considered for comparison. It has been mentioned in the reference that, a phase lag of (Formula) was observed in lift coefficients with respect to motion of the configuration for a free stream Mach number of 0.3 with other conditions remaining the same. The unsteady lift coefficients obtained using KFMG code as well as those available in literature are plotted for the same flow conditions. Approximately the same phase lag of (Formula) is present (for (Formula)) between the lift coefficient curves of KFMG and due to Nixon et al. The phase lag corrected plot of lift coefficient obtained by Nixon et al. is compared with the lift coefficient versus time obtained by 3-D KFMG Euler code. The two results compare well except that the peaks are over predicted by KFMG code. It is nut clear at this stage whether our results should at all match with those due to Nixon et al. Further in depth study is obviously required to settle the issue. Thus the Kinetic Flux Vector Splitting on Moving Grids has been found to be a very good and a sound method for splitting fluxes and is a generalisation of earlier KFVS on fixed grids. It has been found to be very successful in numerical simulation of unsteady aerodynamics and computational aeroelasticity.

Analysis of unsteady flows is a very challenging topic of research. A decade ago, potential flow equations were used to predict unsteady pressures on oscillating bodies. Recognising the fact that nonlinear aerodynamics is essential to analyse unsteady flows accurately, particularly in transonic and supersonic flows, different Euler formulations operating on moving grids have emerged recently as important CFD tools for unsteady aerodynamics. Numerical solution of Euler equations on moving grids based on upwind schemes such as the ones due to van Leer and Roe have been developed for the purpose of numerical simulation of unsteady transonic and supersonic flows. In the present work, Euler computations based on yet another recent robust upwind scheme (for steady flows) namely Kinetic Flux Vector Splitting (KFVS) scheme due to Deshpande and Mandal is chosen for further development of a time accurate Euler solver to operate on problems involving moving boundaries. The development of an Euler code based on this scheme is likely to be highly useful to analyse problems of unsteady aerodynamics and computational aeroelasiticity especially when it is noted that KFVS has been found to be an extremely robust scheme for computation of subsonic, transonic, supersonic and hypersonic flows. The KFVS scheme, basically exploits the connection between the linear scalar Boltzmann equation of kinetic theory of gases and the nonlinear vector conservation law, that is, Euler equations of fluid dynamics through moment method strategy. The KFVS scheme has inherent simplicity in splitting the flux even on moving grids due to underlying particle model. The inherent simplicity of KFVS for moving grid problems is due to its relationship with the Boltzmann equation. If a surface is moving with velocity w and a particle has velocity v, then it is quite reasonable to do the splitting based on (v-w)<0 or >0. Only particles having velocity v greater than w will cross the moving surface from left to right and similar arguments hold good for particles moving in opposite direction. It is therefore quite natural to extend KFVS by splitting the Maxwellian velocity distribution at Boltzmann level based on the sign of the normal component of the relative velocity. The relative velocity is the difference between the molecular velocity (v) and the velocity of the moving surface(w). This inherent simplicity of the Kinetic Flux Vector Splitting scheme on Moving Grids (KFMG) method has prompted us to extend the same ideas to 2-D and 3-D problems leading to the present KFMG method. If w is set to zero then KFMG formulation reduces to the one corresponding to KFVS. Thus KFMG formulations axe generalisation of the KFVS formulation. In 2-D and 3-D cases, in addition to the KFMG formulation, the method to move the grids, the appropriate boundary conditions for treating moving surfaces and techniques to improve accuracy in space and time are required to be developed. The 2-D and 3-D formulations based on Kinetic Flux Vector Splitting scheme on Moving Grids method have been developed for computing unsteady flows. Between two successive time steps, the body changes its orientation in case of an oscillation or it deforms when subjected to, aerodynamic loads. In either of these cases the grid corresponding to the first time step has to be moved or regenerated around the displaced or deformed body. There are several approaches available to generate grids around moving bodies. In the present work, the 'spring analogy method' is followed to obtain grid around deflected geometries within the frame work of structured grid. Using this method, the grids are moved from previous time to the current time. This method is capable of tackling any kind of aeroelastic deformation of the body. For oscillating bodies, a suitable boundary condition enforcing the flow tangency on the body needs to be developed. As a first attempt, the body surface has been treated as an 1-D piston undergoing compression and expansion. Then, a more general Kinetic Moving Boundary Condition(KMBC) has been developed. The KMBC uses specular reflection model of kinetic theory of gases. In order to treat fixed outer boundary, Kinetic Outer Boundary Condition(KOBC) has been applied. The KOBC is more general in the sense that, it can treat different type of boundaries (subsonic, supersonic, inflow or out flow boundary). A 2-D cell-centered finite volume KFMG Euler code to operate on structured grid has been developed. The time accuracy is achieved by incorporating a fourth order Runge-Kutta time marching method. The space accuracy has been enhanced by using high resolution scheme as well as second order scheme using the method of reconstruction of fluxes. First, the KFMG Euler code has been applied to standard test cases for computing steady flows around NACA 0012 and NACA 64AQ06 airfoils in transonic flow. For these two airfoils both computational and experimental results are available in literature. It is thus possible to verify (that is, prove the claim that code is indeed solving the partial differential equations + boundary conditions posed to the code) and validate(that is, comparison with experimental results) the 2-D KFMG Euler code. Having verified and validated the 2-D KFMG Euler code for the standard test cases, the code is then applied to predict unsteady flows around sinusoidally oscillating NACA 0012 and NACA 64A006 airfoils in transonic flow. The computational and experimental unsteady results are available in literature for these airfoils for verification and validation of the present results. The unsteady lift and normal force coefficients have been predicted fairly accurately by all the CFD codes. However there is some difficulty about accurate prediction of unsteady pitching moment coefficient. Even Navier-Stokes code could not predict pitching moment accurately. This issue needs further in depth study and probably intensive computation which have not been undertaken in the present study. Next, a two degrees of £reedom(2-DOF) structural dynamics model of an airfoil undergoing pitch and plunge motions has been coupled with the 2-D KFMG Euler code for numerical simulation of aeroelastic problems. This aeroelastic analysis code is applied to NACA 64A006 airfoil undergoing pitch and plunge motions in transonic flow to obtain aeroelastic response characteristics for a set of structural parameters. For this test case also computed results are available in literature for verification. The response characteristics obtained have showed three modes namely stable, neutrally stable and unstable modes of oscillations. It is interesting to compare the value of airfoil-to-air mass ratio (Formula) obtained by us for neutrally stable condition with similar values obtained by others and some differences between them are worth mentioning here. The values of \i for neutral stability are different for different authors. The differences in values of (Formula) predicted by various authors are primarily due to differences which can be due to grid as well as mathematical model used. For example, the Euler calculations, TSP calculations and full potential calculations always show differences in shock location for the same flow problem. Changes in shock location will cause change in pressure distribution on airfoil which in turn will cause changes in values of \L for conditions of neutral stability. The flutter speed parameter(U*) has also been plotted with free stream Mach number for two different values of airfoil - to - air mass ratio. These curves shown a dip when the free stream Mach number is close to 0.855. This is referred as "Transonic Dip Phenomenon". The shock waves play a dominant role in the mechanism of transonic dip phenomenon. Lastly, cell-centered finite volume KFMG 3-D Euler code has been developed to operate on structured grids. The time accuracy is achieved by incorporating a fourth order Runge-Kutta method. The space accuracy has been enhanced by using high resolution scheme. This code has 3-D grid movement module which is based on spring analogy method. The KMBC to treat oscillating 3-D configuration and KOBC for treating 3-D outer boundary have also been formulated and implemented in the code. The 3-D KFMG Euler code has been first verified and validated for 3-D steady flows around standard shapes such as, transonic flow past a hemisphere cylinder and ONERA M6 wing. This code has also been used for predicting hypersonic flow past blunt cone-eylinder-flare configuration for which experimental data are available. Also, for this case, the results are compared with a similar Euler code. Then the KFMG Euler code has been used for predicting steady flow around ogive-cylinder-ogive configuration with elliptical cross section. The aerodynamic coefficients obtained have been compared with those of another Euler code. Thus, the 3-D KFMG Euler code has been verified and validated extensively for steady flow problems. Finally, the 3-D KFMG based Euler code has been applied to an oscillating ogive-cylinder-ogive configuration in transonic flow. This test case has been chosen as it resembles the core body of a flight vehicle configuration of interest to DRDO,India. For this test case, the unsteady lift coefficients are available in literature for verifying the present results. Two grid sizes are used to perform the unsteady calculations using the present KFMG 3-D Euler code. The hysteresis loops of lift and moment coefficients confirmed the unsteady behaviour during the oscillation of the configuration. This has proved that, the 3-D formulations are capable of predicting the unsteady flows satisfactorily. The unsteady results obtained for a grid with size of 45x41x51 which is very close to the grid size chosen in the reference(Nixon et al.) are considered for comparison. It has been mentioned in the reference that, a phase lag of (Formula) was observed in lift coefficients with respect to motion of the configuration for a free stream Mach number of 0.3 with other conditions remaining the same. The unsteady lift coefficients obtained using KFMG code as well as those available in literature are plotted for the same flow conditions. Approximately the same phase lag of (Formula) is present (for (Formula)) between the lift coefficient curves of KFMG and due to Nixon et al. The phase lag corrected plot of lift coefficient obtained by Nixon et al. is compared with the lift coefficient versus time obtained by 3-D KFMG Euler code. The two results compare well except that the peaks are over predicted by KFMG code. It is nut clear at this stage whether our results should at all match with those due to Nixon et al. Further in depth study is obviously required to settle the issue. Thus the Kinetic Flux Vector Splitting on Moving Grids has been found to be a very good and a sound method for splitting fluxes and is a generalisation of earlier KFVS on fixed grids. It has been found to be very successful in numerical simulation of unsteady aerodynamics and computational aeroelasticity.

Ultra-fast laser heating of nano-films is investigated using 3-D Dual Phase Lag heat transport equation with laser heating at different locations on the metal film. The energy absorption rate, which is used to model femtosecond laser heating, is modified to accommodate for three-dimensional laser heating. A numerical solution based on an explicit finite-difference method is employed to solve the DPL equation. The stability criterion for selecting a time step size is obtained using von Neumann eigenmode analysis, and grid function convergence tests are performed. DPL results are compared with classical diffusion and hyperbolic heat conduction models and significant differences among these three approaches are demonstrated. We also develop an implicit finite-difference scheme of Crank-Nicolson type for solving 1-D and 3-D DPL equations. The proposed numerical technique solves one equation unlike other techniques available in the literature, which split the DPL equation into a system of two equations and then apply discretization. Stability analysis is performed using a von Neumann stability analysis. In 3-D, the discretized equation is solved using delta-form Douglas and Gunn time splitting. The performance of the proposed numerical technique is compared with the numerical techniques available in the literature.

Ces dernières années, l’intelligence artificielle (IA) est confrontée à deux défis majeurs (parmi d’autres), à savoir l’explicabilité et la frugalité, dans un contexte d’intégration de l’IA dans des systèmes critiques ou embarqués et de raréfaction des ressources. Le défi est d’autant plus conséquent que les modèles proposés apparaissent commes des boîtes noires étant donné le nombre faramineux d’hyperparamètres à régler (véritable savoir-faire) pour les faire fonctionner. Parmi ces paramètres, l’optimiseur ainsi que les réglages qui lui sont associés ont un rôle critique dans la bonne mise en oeuvre de ces outils [196]. Dans cette thèse, nous nous focalisons sur l’analyse des algorithmes d’apprentissage/optimiseurs dans le contexte des réseaux de neurones, en identifiant des propriétés mathématiques faisant écho aux deux défis évoqués et nécessaires à la robustesse du processus d’apprentissage. Dans un premier temps, nous identifions des comportements indésirables lors du processus d’apprentissage qui vont à l’encontre d’une IA explicable et frugale. Ces comportements sont alors expliqués au travers de deux outils: la stabilité de Lyapunov et les intégrateurs géométriques. Empiriquement, la stabilisation du processus d’apprentissage améliore les performances, autorisant la construction de modèles plus économes. Théoriquement, le point de vue développé permet d’établir des garanties de convergence pour les optimiseurs classiquement utilisés dans l’entraînement des réseaux. La même démarche est suivie concernant l’optimisation mini-batch où les comportements indésirables sont légions: la notion de splitting équilibré est alors centrale afin d’expliquer et d’améliorer les performances. Cette étude ouvre la voie au développement de nouveaux optimiseurs adaptatifs, issus de la relation profonde entre optimisation robuste et schémas numériques préservant les invariants des systèmes dynamiques
Over the last few years, developping an explainable and frugal artificial intelligence (AI) became a fundamental challenge, especially when AI is used in safety-critical systems and demands ever more energy. This issue is even more serious regarding the huge number of hyperparameters to tune to make the models work. Among these parameters, the optimizer as well as its associated tunings appear as the most important leverages to improve these models [196]. This thesis focuses on the analysis of learning process/optimizer for neural networks, by identifying mathematical properties closely related to these two challenges. First, undesirable behaviors preventing the design of explainable and frugal networks are identified. Then, these behaviors are explained using two tools: Lyapunov stability and geometrical integrators. Through numerical experiments, the learning process stabilization improves the overall performances and allows the design of shallow networks. Theoretically, the suggested point of view enables to derive convergence guarantees for classical Deep Learning optimizers. The same approach is valuable for mini-batch optimization where unwelcome phenomenons proliferate: the concept of balanced splitting scheme becomes essential to enhance the learning process understanding and improve its robustness. This study paves the way to the design of new adaptive optimizers, by exploiting the deep relation between robust optimization and invariant preserving scheme for dynamical systems

Lors que nous examinons numériquement des phénomènes multiphasiques suite à un accidentgrave dans le réacteur nucléaire, la dimension caractéristique des zones multi-fluides(non-réactifs et réactifs) s'avère beaucoup plus petite que celle du bâtiment réacteur, cequi fait la Simulation Numérique Directe de la configuration à peine réalisable. Autrement,nous proposons de considérer la zone de mélange multiphasique comme une interface infinimentfine. Puis, le solveur de Riemann réactif est inséré dans la Méthode des ÉquationsDiscrètes Réactives (RDEM) pour calculer le front de combustion à grande vitesse représentépar une interface discontinue. Une approche anti-diffusive est ensuite couplée avec laRDEM afin de précisément simuler des interfaces réactives. La robustesse et l'efficacité decette approche en calculant tant des interfaces multiphasiques que des écoulements réactifssont à la fois améliorées grâce à la méthode ici proposée : upwind downwind-controlled splitting(UDCS). UDCS est capable de résoudre précisément des interfaces avec les maillagesnon-structurés multidimensionnels, y compris des fronts réactifs de détonation et de déflagration.

Multi-User Multi-Input Multi-Output (MU-MIMO) systems are considered to be the sustainable technologies of the current and future of the upcoming wireless and mobile networks generations. The perspectives of these technologies under several scenarios is the focus of the present thesis. The initial system model covers the MU-MIMO, especially in the massive form that is considered to be the promising ideas and pillars of the 5G network. It is observed that the optimal number of users should be served in the time-frequency resource even though the maximum limitation of the MU-MIMO is governed by the total receiving antennas (K) is less than or equal to the base station antennas (M). The system capacity of the massive MIMO (mMIMO) under perfect channel state information (CSI) of uncorrelated channel is investigated and studied. Two types of precoders were applied, one is directly based on channel inversion, and the other uses the Eigen decomposition that is derived subject to the signal to a leakage maximization problem. The two precoders show a degree of equivalency under certain assumptions for the number of antennas at the user end. The convex optimization of multi-antenna networks to achieve the design model of optimum beamformer (BF) based on the uniform linear array (ULA) is studied. The ULA is selected for its simplicity to analyse many scenarios and its importance to match the future network applied millimetre wave (mmWave) spectrum. The maximum beams generated by the ULA are explored in terms of several physical system parameters. The duality between the MU-MIMO and ULA and how they are related based on beamformer operation are detailed and discussed. Finally, two approaches for overloaded systems are presented when the availability of massive array that is not guaranteed due to physical restrictions since the existence of a large number of devices will result in breaking the dimension rule (i.e., K ≤ M). As a solution, a low complexity users selection algorithm is proposed. The channel considered is uncorrelated with full and perfect knowledge at the BS. In particular, these two channel conditions may not be available in all scenarios. The CSI may be imperfect, and even the instantaneous form does not exist. A hybrid precoder between the mixed CSI (includes imperfect and statistical) and rate splitting approach is proposed to deal with an overloaded system under a low number of BS antennas.
Ministry of Higher Education and Scientific Research of Iraq

Denna systematiska litteraturstudie syftar till att med hjälp av forskning identifiera avgörande faktorer för framgångsrika undervisningsstrategier av stambråk i grundskolans matematikundervisning. Studien baseras på elva vetenskapliga artiklar som bearbetats systematiskt med hjälp av innehållsanalys för att besvara forsknings-frågorna om vilka avgörande faktorer som forskningen visar för undervisningen av stambråk samt vilka framgångsrika undervisningsstrategier som finns. Forskningen visar att areamodellen som representationsform dominerar undervisningen av bråk vilket innebär att stambråk får lite plats i undervisningen. Stambråket är en viktig del för att kunna tillägna sig avgörande faktorer av bråk. Resultatet visar att en undervisning med linear measurement (linjära representationsformer) betonar stambråkets roll som tolkningsverktyg för att kunna jämföra andra bråk samt det omvända förhållandet där en större nämnare utgör en mindre andel. Resultatet visar också att undervisningen av stambråk etablerar grundläggande principer för rationella tal och mer avancerade matematiska områden som proportionalitet och algebra. Därmed är lärares val av undervisningsstrategier och representationsformer samt deras kunskaper inom dessa områden vitala för vad eleverna kan tillägna sig i samband med bråkundervisningen.

This thesis presents the construction, the analysis and the verification of a new form of higher than second order fluctuation splitting discretisation for the solution of steady conservation laws on unstructured meshes. This is an alternative approach to the two existing higher than second order fluctuation splitting schemes, which use submesh reconstruction (developed by Abgrall and Roe) and gradient recovery (developed by Caraemi) to obtain the loacl higher degree polynomials used to evaluate the fluctuation. The new higher than second order approach constructs the polynomial interpolant of the values of the dependent variables at an appropriate number of carefully chosen mesh nodes. As they stand, none of the higher than second order methods can guarantee the absence of spurious oscillations from the flow without the application of an additional smoothing stage. The implementation of a technique that removes unphysical oscillations (devised by Hubbard) as part of a new higher than second order approach will be outlined. The design steps and theoretical bases are discussed in depth. The new higher than second order approach is examined and analysed through application to a series of linear and nonlinear scalar problems, using a pseudo-time-stepping technique to reach steady state solution on two-dimensional structured and unstructured meshes. The results demonstrate its effectiveness in approximating the linear and nolinear scalar problems. This thesis also addresses the development and examination of a multistage high order (in space and time) fluctuation splitting scheme for two-dimensional unsteady scalar advection on triangular unstructured meshes. the method is similar in philosophy to that of multistep high order (in space and time) fluctuation splitting scheme for the approximation of time-dependent hyperbolic conservation laws. The construction and implementation of the high order multistage time-dependent method are discussed in detail and its performance is illustrated using several standard test problems. The multistage high order time-dependent method is evaluated in the context of existing fluctuation splitting approaches to modelling time-dependent problems and some suggestions for their future development are made. Results presented indicate that the multistage high orer method can produce a slightly more accurate solution than the multistep high order method.

High-resolution shock-capturing schemes (HRSC) are known to be the most adequate and advanced technique used for numerical approximation to the solution of hyperbolic systems of conservation laws. Since most of the astrophysical phenomena can be described by means of system of (M)HD conservation equations, nding most accurate, computationally not expensive and robust numerical approaches for their solution is a task of great importance for numerical astrophysics. Based on the Central Weighted Non-Oscillatory (CWENO) reconstruction approach, which relies on the adaptive choice of the smoothest stencil for resolving strong shocks and discontinuities in central framework on staggered grid, we present a new algorithm for systems of conservation laws using the key idea of evolving the intermediate stages in the Runge Kutta time discretization in primitive variables . In this thesis, we introduce a new so-called conservative-primitive variables strategy (CPVS) by integrating the latter into the earlier proposed Central Runge Kutta schemes (Pareschi et al., 2005). The advantages of the new shock-capturing algorithm with respect to the state-of-the-art HRSC schemes used in astrophysics like upwind Godunov-type schemes can be summarized as follows: (i) Riemann-solver-free central approach; (ii) favoring dissipation (especially needed for multidimensional applications in astrophysics) owing to the di ffusivity coming from the design of the scheme; (iii) high accuracy and speed of the method. The latter stems from the fact that the advancing in time in the predictor step does not need inversion between the primitive and conservative variables and is essential in applications where the conservative variables are neither trivial to compute nor to invert in the set of primitive ones as it is in relativistic hydrodynamics. The main objective of the research adopted in the thesis is to outline the promising application of the CWENO (with CPVS) in the problems of the computational astrophysics. We tested the method for one dimensional Euler hydrodynamics equations and we assessed the advantages against the operator splitting and finite-volume Godunov-type approaches implemented in the widely used astrophysical codes ZEUSMP/ 2 (Stone and Norman, 1992) and ATHENA (Stone et al., 2008), respectively. We extended the application of the scheme to one dimensional relativistic hydrodynamics (RHD), which (to the author's knowledge) is the fi rst successful attempt to approximate the special relativistic hydrodynamics with CWENO method. We demonstrate that strong discontinuities can be captured within two numerical zones and prevent the onset of numerical oscillations. In the second part of the present thesis, the astrophysical operator-splitting MHD code ZEUS-MP/2 has been used to perform three dimensional nonlinear simulations of MHD instabilities. First, we present global 3D nonlinear simulations of the Tayler instability in the presence of vertical elds. The initial con guration is in equilibrium, which is achieved by balancing a pressure gradient with the Lorentz force. The nonlinear evolution of the system leads to stable equilibrium with current free toroidal eld. We nd that the presence of a vertical poloidal eld stabilizes the system in the range from B phi approximately of order of Bz to higher values of Bz (Ivanovski and Bonanno, 2009). Second, the dynamics of the expansion of two colliding plasma plumes in ambient gas has been investigated via hydrodynamical simulations. Experimental observations of a single plume, generated by high power pulsed laser ablation of a solid target in ambient gas with pressure of about 10^-1 Torr, show possible Rayleigh-Taylor (RT) instability. Our numerical simulations with two plumes show RT instability even in low pressure gas, where single-plume expansion cannot cause instability. In addition, we nd that the RT instability is developed for about ten nanoseconds, while the instability in the case of a single plume typically takes thousand of nanoseconds. We show that the theoretically derived density condition for stability, Rho_plume < Rho_gas, is satis ed in all our simulations (Ivanovski et al., 2010). In the present thesis, we con rm the promising behavior of the conservative-primitive variables strategy with CWENO approach in computational astrophysics. We demonstrated high accuracy and robustness of the method in the essential one dimensional applications, sod-shock tubes and slow-moving shocks. Extending the method to higher dimensions and using the knowledge accumulated by means of direct numerical operator splitting simulations of MHD instabilities motivates building a modern accurate astrophysical code which will be able to resolve a wide range of problems, from ideal (magneto)hydrodynamics to relativistic (magneto)hydrodynamics.

Molecular dynamics (MD) computations aim to simulate materials at the atomic level by approximating molecular interactions classically, relying on the Born-Oppenheimer approximation and semi-empirical potential energy functions as an alternative to solving the difficult time-dependent Schrodinger equation. An approximate solution is obtained by discretization in time, with an appropriate algorithm used to advance the state of the system between successive timesteps. Modern MD simulations simulate complex systems with as many as a trillion individual atoms in three spatial dimensions. Many applications use MD to compute ensemble averages of molecular systems at constant temperature. Langevin dynamics approximates the effects of weakly coupling an external energy reservoir to a system of interest, by adding the stochastic Ornstein-Uhlenbeck process to the system momenta, where the resulting trajectories are ergodic with respect to the canonical (Boltzmann-Gibbs) distribution. By solving the resulting stochastic differential equations (SDEs), we can compute trajectories that sample the accessible states of a system at a constant temperature by evolving the dynamics in time. The complexity of the classical potential energy function requires the use of efficient discretization schemes to evolve the dynamics. In this thesis we provide a systematic evaluation of splitting-based methods for the integration of Langevin dynamics. We focus on the weak properties of methods for confiurational sampling in MD, given as the accuracy of averages computed via numerical discretization. Our emphasis is on the application of discretization algorithms to high performance computing (HPC) simulations of a wide variety of phenomena, where configurational sampling is the goal. Our first contribution is to give a framework for the analysis of stochastic splitting methods in the spirit of backward error analysis, which provides, in certain cases, explicit formulae required to correct the errors in observed averages. A second contribution of this thesis is the investigation of the performance of schemes in the overdamped limit of Langevin dynamics (Brownian or Smoluchowski dynamics), showing the inconsistency of some numerical schemes in this limit. A new method is given that is second-order accurate (in law) but requires only one force evaluation per timestep. Finally we compare the performance of our derived schemes against those in common use in MD codes, by comparing the observed errors introduced by each algorithm when sampling a solvated alanine dipeptide molecule, based on our implementation of the schemes in state-of-the-art molecular simulation software. One scheme is found to give exceptional results for the computed averages of functions purely of position.

Cette thèse s’inscrit dans le domaine mathématique de l’analyse des équations aux dérivées partielles (EDP) non-linéaires stochastiques. Nous nous intéressons à des EDP paraboliques et hyperboliques que l’on perturbe stochastiquement au sens d’Itô. Il s’agit d’introduire l’aléatoire via l’ajout d’une intégrale stochastique (intégrale d’Itô) qui peut dépendre ou non de la solution, on parle alors de bruit multiplicatif ou additif. La présence de la variable de probabilité ne nous permet pas d’utiliser tous les outils classiques de l’analyse des EDP. Notre but est d’adapter les techniques connues dans le cadre déterministe aux EDP non linéaires stochastiques en proposant des méthodes alternatives. Les résultats obtenus sont décrits dans les cinq chapitres de cette thèse : Dans le Chapitre I, nous étudions une perturbation stochastique des équations de Barenblatt. En utilisant une semi- discrétisation implicite en temps, nous établissons l’existence et l’unicité d’une solution dans le cas additif, et grâce aux propriétés de la solution nous sommes en mesure d’étendre ce résultat au cas multiplicatif à l’aide d’un théorème de point fixe. Dans le Chapitre II, nous considérons une classe d’équations de type Barenblatt stochastiques dans un cadre abstrait. Il s’agit là d’une généralisation des résultats du Chapitre I. Dans le Chapitre III, nous travaillons sur l’étude du problème de Cauchy pour une loi de conservation stochastique. Nous montrons l’existence d’une solution par une méthode de viscosité artificielle en utilisant des arguments de compacité donnés par la théorie des mesures de Young. L’unicité repose sur une adaptation de la méthode de dédoublement des variables de Kruzhkov.. Dans le Chapitre IV, nous nous intéressons au problème de Dirichlet pour la loi de conservation stochastique étudiée au Chapitre III. Le point remarquable de l’étude repose sur l’utilisation des semi-entropies de Kruzhkov pour montrer l’unicité. Dans le Chapitre V, nous introduisons une méthode de splitting pour proposer une approche numérique du problème étudié au Chapitre IV, suivie de quelques simulations de l’équation de Burgers stochastique dans le cas unidimensionnel
This thesis deals with the mathematical field of stochastic nonlinear partial differential equations’ analysis. We are interested in parabolic and hyperbolic PDE stochastically perturbed in the Itô sense. We introduce randomness by adding a stochastic integral (Itô integral), which can depend or not on the solution. We thus talk about a multiplicative noise or an additive one. The presence of the random variable does not allow us to apply systematically classical tools of PDE analysis. Our aim is to adapt known techniques of the deterministic setting to nonlinear stochastic PDE analysis by proposing alternative methods. Here are the obtained results : In Chapter I, we investigate on a stochastic perturbation of Barenblatt equations. By using an implicit time discretization, we establish the existence and uniqueness of the solution in the additive case. Thanks to the properties of such a solution, we are able to extend this result to the multiplicative noise using a fixed-point theorem. In Chapter II, we consider a class of stochastic equations of Barenblatt type but in an abstract frame. It is about a generalization of results from Chapter I. In Chapter III, we deal with the study of the Cauchy problem for a stochastic conservation law. We show existence of solution via an artificial viscosity method. The compactness arguments are based on Young measure theory. The uniqueness result is proved by an adaptation of the Kruzhkov doubling variables technique. In Chapter IV, we are interested in the Dirichlet problem for the stochastic conservation law studied in Chapter III. The remarkable point is the use of the Kruzhkov semi-entropies to show the uniqueness of the solution. In Chapter V, we introduce a splitting method to propose a numerical approach of the problem studied in Chapter IV. Then we finish by some simulations of the stochastic Burgers’ equation in the one dimensional case

This study investigates the accuracy and efficiency of several flux splitting methods for the compressible, two-dimensional Euler equations. Steger-Warming flux vector splitting method, Van Leer flux vector splitting method, The Advection Upstream Splitting Method (AUSM), Artificially Upstream Flux Vector Splitting Scheme (AUFS) and Roe&rsquo
s flux difference splitting schemes were implemented using the first- and second-order reconstruction methods. Limiter functions were embedded to the second-order reconstruction methods. The flux splitting methods are applied to subsonic, transonic and supersonic flows over NACA0012 airfoil, as well as subsonic, transonic and supersonic flows in a channel. The comparison of the obtained results with each other and the ones in the literature is presented. The advantages and disadvantages of each scheme among others are identified.

Depuis l’article fondateur de Jordan, Kinderlehrer et Otto en 1998, il est bien connu qu’une large classe d’équations paraboliques peuvent être vues comme des flots de gradient dans l’espace de Wasserstein. Le but de cette thèse est d’étendre cette théorie à certaines équations et systèmes qui n’ont pas exactement une structure de flot de gradient. Les interactions étudiées sont de différentes natures. Le premier chapitre traite des systèmes avec des interactions non locales dans la dérive. Nous étudions ensuite des systèmes de diffusions croisées s’appliquant aux modèles de congestion pour plusieurs populations. Un autre modèle étudié est celui où le couplage se trouve dans le terme de réaction comme les systèmes proie-prédateur avec diffusion ou encore les modèles de croissance tumorale. Nous étudierons enfin des systèmes de type nouveau où l’interaction est donnée par un problème de transport multi-marges. Une grande partie de ces problèmes est illustrée de simulations numériques
Since 1998 and the seminal work of Jordan, Kinderlehrer and Otto, it is well known that a large class of parabolic equations can be seen as gradient flows in the Wasserstein space. This thesis is devoted to extensions of this theory to equations and systems which do not have exactly a gradient flow structure. We study different kind of couplings. First, we treat the case of nonlocal interactions in the drift. Then, we study cross diffusion systems which model congestion for several species. We are also interested in reaction-diffusion systems as diffusive prey-predator systems or tumor growth models. Finally, we introduce a new class of systems where the interaction is given by a multi-marginal transport problem. In many cases, we give numerical simulations to illustrate our theorical results

The computation of Schrödinger equations in the semiclassical regime presents several enduring challenges due to the presence of the small semiclassical parameter. Standard approaches for solving these equations commence with spatial discretisation followed by exponentiation of the discretised Hamiltonian via exponential splittings. In this thesis we follow an alternative strategy${-}$we develop a new technique, called the symmetric Zassenhaus splitting procedure, which involves directly splitting the exponential of the undiscretised Hamiltonian. This technique allows us to design methods that are highly efficient in the semiclassical regime. Our analysis takes place in the Lie algebra generated by multiplicative operators and polynomials of the differential operator. This Lie algebra is completely characterised by Jordan polynomials in the differential operator, which constitute naturally symmetrised differential operators. Combined with the $\mathbb{Z}_2$-graded structure of this Lie algebra, the symmetry results in skew-Hermiticity of the exponents for Zassenhaus-style splittings, resulting in unitary evolution and numerical stability. The properties of commutator simplification and height reduction in these Lie algebras result in a highly effective form of $\textit{asymptotic splitting:} $exponential splittings where consecutive terms are scaled by increasing powers of the small semiclassical parameter. This leads to high accuracy methods whose costs grow quadratically with higher orders of accuracy. Time-dependent potentials are tackled by developing commutator-free Magnus expansions in our Lie algebra, which are subsequently split using the Zassenhaus algorithm. We present two approaches for developing arbitrarily high-order Magnus--Zassenhaus schemes${-}$one where the integrals are discretised using Gauss--Legendre quadrature at the outset and another where integrals are preserved throughout. These schemes feature high accuracy, allow large time steps, and the quadratic growth of their costs is found to be superior to traditional approaches such as Magnus--Lanczos methods and Yoshida splittings based on traditional Magnus expansions that feature nested commutators of matrices. An analysis of these operatorial splittings and expansions is carried out by characterising the highly oscillatory behaviour of the solution.

On étudie dans le cadre de la thèse une famille de schémas numériques permettant de résoudre les équations de Saint-Venant. Ces schémas utilisent une décomposition d'opérateur de type Lagrange-projection afin de séparer les ondes de gravité et les ondes de transport. Un traitement implicite du système acoustique (relié aux ondes de gravité) permet aux schémas de rester stable avec de grands pas de temps. La correction des flux de pression rend possible l'obtention d'une solution approchée précise quel que soit le régime d'écoulement vis-à-vis du nombre de Froude. Une attention toute particulière est portée sur le traitement du terme source qui permet la prise en compte de l'influence de la topographie. On obtient notamment la propriété dite équilibre permettant de conserver exactement certains états stationnaires, appelés état du "lac au repos". Des versions 1D et 2D sur maillages non-structurés de ces méthodes ont été étudiées et implémentées dans un cadre volumes finis. Enfin, une extension vers des méthodes ordres élevés Galerkin discontinue a été proposée en 1D avec des limiteurs classiques ainsi que combinée avec une boucle MOOD de limitation a posteriori
In this thesis we study a family of numerical schemes solving the shallow water equations system. These schemes use a Lagrange-projection like splitting operator technique in order to separate the gravity waves and the transport waves. An implicit-explicit treatment of the acoustic system (linked to the gravity waves) allows the schemes to stay stable with large time step. The correction of the pressure fluxes enables the obtain of a precise approximation solution whatever the regime flow is with respect to the Froude number. A particular attention has been paid over the source term treatment which permits to take the topography into account. We especially obtain the so-called well-balanced property giving the exact conservation of some steady states, namely the "lake at rest" state. 1D and 2D versions of this methods have been studied and implemented in the finite volumes framework. Finally, a high order discontinuous Galerkin extension has been proposed in 1D with classical limiters along with a combined MOOD loop a posteriori limiting strategy

In this dissertation the heat flux prediction capabilities of Residual Distribution (RD) schemes for hypersonic flow fields are investigated. Two canonical configurations are considered: the flat plate and the blunt body (cylinder) problems, with a preference for the last one. Both simple perfect gas and more complex thermo-chemical non-equilibrium (TCNEQ) thermodynamic models have been considered.

The unexpected results identified early in the investigation lead to a thorough analysis to identify the causes of the unphysical hypersonic heating.

The first step taken is the assessment of the quality of flow field and heat transfer predictions obtained with RD methods for subsonic configurations. The result is positive, both for flat plate and cylinder configurations, as RD schemes produce accurate flow solutions and heat flux predictions whenever no shock waves are present, irrespective of the gas model employed.

Subsonic results prove that hypersonic heating anomalies are a consequence of the presence of a shock wave in the domain and/or the way it is handled numerically.

Regarding hypersonic flows, the carbuncle instability is discarded first as the cause of the erroneous stagnation heating. The anomalies are shown next to be insensitive to the kind and level of dissipation introduced via the (quasi-)positive contribution P to blended B schemes. Additionally, insufficient mesh resolution locally over the region where the shock wave is captured numerically is found to be irrelevant.

Capturing the bow shock in a manner that total enthalpy is preserved immediately before and after the numerical shock wave is, on the contrary, important for correct heating prediction.

However, a carefully conceived shock capturing term is, by itself, not sufficient to guarantee correct heating predictions, since the LP scheme employed (be it stand-alone in a shock fitting context or combined into a blended scheme for a shock capturing computation) needs to be immune to spurious recirculations in the stagnation point.

Once the causes inducing the heating anomalies identified, hypersonic shocked flows in TCNEQ conditions are studied.

In order to alleviate the computational effort necessary to handle many species non-equilibrium (NEQ) models, the extension of an entropic (or symmetrizing) variables formulation RD to the nS species, two temperature TCNEQ model is accomplished, and the savings in computational time it allows are demonstrated.

The multi-dimensional generalization of Roe-like linearizations for the TCNEQ model is addressed next: a study on the existence conditions of the linearized state guaranteeing discrete conservation is conducted.

Finally, the new dissipative terms derived for perfect gas are adapted to work under TCNEQ conditions; the resulting numerical schemes are free of the temperature undershoot and Mach number overshoot problem afflicting standard CRD schemes.
Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished

Interacting species systems have complex dynamics that are often subject to change due to internal and external factors. Quantitative modelling approaches to capture demographic fluctuations can be insufficient in the presence of stochastic variation and uncertainty. This thesis establishes new modelling techniques to account for such demographic variations and develops novel numerical simulation tools for solving these systems. These explorations are extended for solving invasive species management problems where robust management actions and efficient use of allocated budgets are necessary.

Les modèles numériques d'océans régionaux tridimensionnels sont basés sur la résolution des équations primitives et utilisent pour la plupart des méthodes de résolution eulérienne de type différences finies sur des grilles décalées. Ces modèles doivent représenter fidèlement les transports et transferts d'énergie. L'amélioration de ces modèles numériques exige donc (i) l'identification des processus prépondérants, notamment en terme de dissipation, dans ces transferts et (ii) la construction de méthodes numériques respectant un certain nombre d'équilibres. La première partie du travail se concentre sur la propagation des ondes externes et internes de gravité. Nous nous intéresserons en premier lieu à la stabilité de la séparation en mode rapide (barotrope) et lents (baroclines) et montrons qu'elle peut être ameliorée en levant certaines hypothèses traditionnellement effectuées. Dans un second temps, nous étudions l'impact de la discrétisation (ordre des schémas, grilles décalées ou non) sur la propagation des ondes internes de gravité provenant du couplage vitesse pression. Une décomposition en modes verticaux nous permet également de proposer un schéma espace temps très efficace. La seconde partie étudie en détail les schémas d'advection de quantité de mouvement et de traceurs, tout particulièrement dans l'objectif d'une réduction de la diffusion diapycnale (diffusion dans les directions orthogonales aux couches de densité constante). Ce travail nous amène tout d'abord à porter notre attention sur les schémas d'advection verticaux souvent négligés au regard de la dimension horizontale. Les bonnes propriétés d'un schéma compact (et de ses variantes espace temps et monotones) sont mises en avant. Enfin nous analysons le comportement multidimensionnel de ces schémas d'advection
Three-dimensional regional ocean numerical models are based on solving the primitive equations and mostly use Eulerian finite differences methods of resolution on staggered grids. These models must accurately represent transports and energy transfers. Improving these numerical models therefore requires (i) the identification of predominant process, particularly in terms of dissipation in these transfers and (ii) the construction of numerical methods respecting a number of balances. The first part of the work focuses on the propagation of external and internal gravity waves. We focus primarily on the stability of the separation in fast mode (barotropic) and slow (baroclinic) and show that it can be improved by removing certain assumptions traditionally made. In a second step, we study the impact of the discretization (order of schemes, staggered grids or not) on the propagation of internal gravity waves coming from the coupling velocity pressure. A decomposition into vertical modes also allows us to offer a highly effective space-time scheme. The second part examines in detail the numerical advection schemes of momentum and tracers, especially with the aim of reducing the diapycnal diffusion (diffusion in the orthogonal direction of constant density layers). This work leads us first to focus our attention on the vertical advection schemes often overlooked in front of the horizontal dimension. The good properties of a compact schema (and its space-time and monotonous variants ) are highlighted. Finally we analyze the multidimensional behavior of these advection schemes

Les phénomènes de transport en milieux poreux sont étudiés depuis près de deux siècles, cependant les travaux concernant les milieux fortement poreux sont encore relativement peu nombreux. Les modèles couramment utilisés pour les poreux classiques (lits de grains par exemple) sont peu applicables pour les milieux fortement poreux (les mousses par exemple), un certain nombre d’études ont été entreprises pour combler ce manque. Néanmoins, les résultats expérimentaux et numériques caractérisant les pertes de charge dans les mousses sont fortement dispersés. Du fait des progrès de l’imagerie 3D, une tendance émergente est la détermination des paramètres des lois d’écoulement à partir de simulations directes sur des géométries reconstruites. Nous présentons ici l’utilisation d’une nouvelle approche cinétique pour résoudre localement les équations de Navier-Stokes et déterminer les propriétés d’écoulement (perméabilité, dispersion, ...)
A novel kinetic scheme satisfying an entropy condition is developed, tested and implemented for the simulation of practical problems. The construction of this new entropic scheme is presented. A classical hyperbolic system is approximated by a discrete velocity vector kinetic scheme (with the simplified BGK collisional operator), but applied to an inviscid compressible gas dynamics system with a small Mach number parameter, according to the approach of Carfora and Natalini (2008). The numerical viscosity is controlled, and tends to the physical viscosity of the Navier-Stokes system. The proposed numerical scheme is analyzed and formulated as an explicit finite volume flux vector splitting (FVS) scheme that is very easy to implement. It is close in spirit to Lattice Boltzmann schemes, but it has the advantage to satisfy a discrete entropy inequality under a CFL condition and a subcharacteristic stability condition involving a cell Reynolds number. The new scheme is proved to be second-order accurate in space. We show the efficiency of the method in terms of accuracy and robustness on a variety of classical benchmark tests. Some physical problems have been studied in order to show the usefulness of both schemes. The LB code was successfully used to determine the longitudinal dispersion of metallic foams, with the use of a novel indicator. The entropic code was used to determine the permeability tensor of various porous media, from the Fontainebleau sandstone (low porosity) to a redwood tree sample (high porosity). These results are pretty accurate. Finally, the entropic framework is applied to the advection-diffusion equation as a passive scalar

Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro
Considera-se neste trabalho um modelo matemático para escoamentos com duas e três fases em reservatórios petrolíferos e a modelagem computacional do sistema de equações governantes para a sua solução numérica. Os fluidos são imiscíveis e incompressíveis e as heterogeneidades da rocha reservatório são modeladas estocasticamente. Além disso, é modelado o fenômeno de histerese para a fase óleo via funções de permeabilidades relativas. No caso de escoamentos trifásicos água-óleo-gás a escolha de expressões gerais para as funções de permeabilidades relativas pode levar à perda de hiperbolicidade estrita e, desta maneira, à existência de uma região elíptica ou de pontos umbílicos para o sistema não linear de leis de conservação hiperbólicas que descreve o transporte convectivo das fases fluidas. Como conseqüência, a perda de hiperbolicidade estrita pode levar à existência de choques não clássicos (também chamados de choques transicionais ou choques subcompressivos) nas soluções de escoamentos trifásicos, de difícil simulação numérica. Indica-se um método numérico com passo de tempo fracionário, baseado em uma técnica de decomposição de operadores, para a solução numérica do sistema governante de equações diferenciais parciais que modela o escoamento bifásico água-óleo imiscível em reservatórios de petróleo heterogêneos. Um simulador numérico bifásico água-óleo eficiente desenvolvido pelo grupo de pesquisa no qual o autor está inserido foi modificado com sucesso para incorporar a histerese sob as hipóteses consideradas. Os resultados numéricos obtidos para este caso indicam fortes evidências que o método proposto pode ser estendido para o caso trifásico água-óleo-gás. A técnica de decomposição de operadores em dois níveis permite o uso de passos de tempo distintos para os quatro problemas definidos pelo procedimento de decomposição: convecção, difusão, pressão-velocidade e relaxação para histerese. O problema de transporte convectivo (hiperbólico) das fases fluidas é aproximado por um esquema central de diferenças finitas explícito, conservativo, não oscilatório e de segunda ordem. Este esquema é combinado com elementos finitos mistos, localmente conservativos, para a aproximação dos problemas de transporte difusivo (parabólico) e de pressão-velocidade (elíptico). O operador temporal associado ao problema parabólico de difusão é resolvido fazendo-se uso de uma estratégia implícita de solução (Backward Euler). Uma equação diferencial ordinária é resolvida (analiticamente) para a relaxação relacionada à histerese. Resultados numéricos para o problema bifásico água-óleo em uma dimensão espacial em concordância com resultados semi-analíticos disponíveis na literatura foram reproduzidos e novos resultados em meios heterogêneos, em duas dimensões espaciais, são apresentados e a extensão desta técnica para o caso de problemas trifásicos água-óleo-gás é proposta.
We consider in this work a mathematical model for two- and three-phase flow problems in petroleum reservoirs and the computational modeling of the governing equations for its numerical solution. We consider two- (water-oil) and three-phase (water-gas-oil) incompressible, immiscible flow problems and the reservoir rock is considered to be heterogeneous. In our model, we also take into account the hysteresis effects in the oil relative permeability functions. In the case of three-phase flow, the choice of general expressions for the relative permeability functions may lead to the loss of strict hyperbolicity and, therefore, to the existence of an elliptic region or umbilic points for the system of nonlinear hyperbolic conservation laws describing the convective transport of the fluid phases. As a consequence, the loss of hyperbolicity may lead to the existence of nonclassical shocks (also called transitional shocks or undercompressive shocks) in three-phase flow solutions. We present a new, accurate fractional time-step method based on an operator splitting technique for the numerical solution of a system of partial differential equations modeling two-phase, immiscible water-oil flow problems in heterogeneous petroleum reservoirs. An efficient two-phase water-oil numerical simulator developed by our research group was sucessfuly extended to take into account hysteresis effects under the hypotesis previously annouced. The numerical results obtained by the procedure proposed indicate numerical evidence the method at hand can be extended for the case of related three-phase water-gas-oil flow problems. A two-level operator splitting technique allows for the use of distinct time steps for the four problems defined by the splitting procedure: convection, diffusion, pressure-velocity and relaxation for hysteresis. The convective transport (hyperbolic) of the fluid phases is approximated by a high resolution, nonoscillatory, second-order, conservative central difference scheme in the convection step. This scheme is combined with locally conservative mixed finite elements for the numerical solution of the diffusive transport (parabolic) and the pressure-velocity (elliptic) problems. The time discretization of the parabolic problem is performed by means of the implicit Backward Euler method. An ordinary diferential equation is solved (analytically) for the relaxation related to hysteresis. Two-phase water-oil numerical results in one space dimensional, in which are in a very good agreement with semi-analitycal results available in the literature, were computationaly reproduced and new numerical results in two dimensional heterogeneous media are also presented and the extension of this technique to the case of three-phase water-oil-gas flows problems is proposed.

La simulation numérique est aujourd'hui un outils majeur dans la conception des objets aérodynamiques, que ce soit dans l'aéronautique, l'automobile, l'industrie navale, etc... Un des défis majeurs pour repousser les limites des codes de simulation est d'améliorer leur précision, tout en utilisant une quantité fixe de ressources (puissance et/ou temps de calcul). Cet objectif peut être atteint par deux approches différentes, soit en construisant une discrétisation fournissant sur un maillage donné une solution d'ordre très élevé, soit en construisant un schéma compact et massivement parallélisable, de manière à minimiser le temps de calcul en distribuant le problème sur un grand nombre de processeurs. Dans cette thèse, nous tentons de rassembler ces deux approches par le développement et l'implémentation de Schéma Distribuant le Résidu (RDS) d'ordre très élevé et de compacité maximale. Ce manuscrit commence par un rappel des principaux résultats mathématiques concernant les Lois de Conservation hyperboliques (CLs). Le but de cette première partie est de mettre en évidence les propriétés des solutions analytiques que nous cherchons à approcher, de manière à injecter ces propriétés dans celles de la solution discrète recherchée. Nous décrivons ensuite les trois étapes principales de la construction d'un schéma RD d'ordre très élevé : \begin{itemize} \item la représentation polynomiale d'ordre très élevé de la solution sur des polygones et des polyèdres; \item la description de méthodes distribuant le résidu de faible ordre, compactes et conservatives, consistantes avec une représentation polynomiale des données de très haut degré. Parmi elles, une attention particulière est donnée à la plus simple, issue d'une généralisation du schéma de Lax-Friedrichs (LxF); \item la mise en place d'une procédure préservant la positivité qui transforme tout schéma stable et linéaire, en un schéma non linéaire d'ordre très élevé, capturant les chocs de manière non oscillante. \end{itemize} Dans le manuscrit, nous montrons que les schémas obtenus par cette procédure sont consistants avec la CL considérée, qu'ils sont stables en norme $\L^{\infty}$ et qu'ils ont la bonne erreur de troncature. Même si tous ces développements théoriques ne sont démontrés que dans le cas de CL scalaires, des remarques au sujet des problèmes vectoriels sont faites dès que cela est possible. Malheureusement, lorsqu'on considère le schéma LxF, le problème algébrique non linéaire associé à la recherche de la solution stationnaire est en général mal posé. En particulier, on observe l'apparition de modes parasites de haute fréquence dans les régions de faible gradient. Ceux-ci sont éliminés grâce à un terme supplémentaire de stabilisation dont les effets et l'évaluation numérique sont précisément détaillés. Enfin, nous nous intéressons à une discrétisation correcte des conditions limites pour le schéma d'ordre élevé proposé. Cette théorie est ensuite illustrée sur des cas test scalaires bidimensionnels simples. Afin de montrer la généralité de notre approche, des maillages composés uniquement de triangles et des maillages hybrides, composés de triangles et de quadrangles, sont utilisés. Les résultats obtenus par ces tests confirment ce qui est attendu par la théorie et mettent en avant certains avantages des maillages hybrides. Nous considérons ensuite des solutions bidimensionnelles des équations d'Euler de la dynamique des gaz. Les résultats sont assez bons, mais on perd les pentes de convergence attendues dès que des conditions limite de paroi sont utilisées. Ce problème nécessite encore d'être étudié. Nous présentons alors l'implémentation parallèle du schéma. Celle-ci est analysée et illustrée à travers des cas test tridimensionnel de grande taille. Du fait de la relative nouveauté et de la complexité des problèmes tridimensionels, seuls des remarques qualitatives sont faites pour ces cas test : le comportement global semble être bon, mais plus de travail est encore nécessaire pour définir les propriétés du schémas en trois dimensions. Enfin, nous présentons une extension possible du schéma aux équations de Navier-Stokes dans laquelle les termes visqueux sont traités par une formulation de type Galerkin. La consistance de cette formulation avec les équations de Navier-Stokes est démontrée et quelques remarques au sujet de la précision du schéma sont soulevées. La méthode est validé sur une couche limite de Blasius pour laquelle nous obtenons des résultats satisfaisants. Ce travail offre une meilleure compréhension des propriétés générales des schémas RD d'ordre très élevé et soulève de nouvelles questions pour des améliorations futures. Ces améliorations devrait faire des schémas RD une alternative attractive aux discrétisations classiques FV ou ENO/WENO, aussi bien qu'aux schémas Galerkin Discontinu d'ordre très élevé, de plus en plus populaires.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Neste trabalho é apresentado um novo método acurado com passo de tempo fracionário, baseado em uma técnica de decomposição de operadores, para a solução numérica de um sistema governante de equações diferenciais parciais que modela escoamento trifásico água-gás-óleo imiscível em reservatórios de petróleo heterogêneos no qual os efeitos de compressibilidade do gás não foram levados em conta. A técnica de decomposição de operadores em dois níveis permite o uso de passos de tempo distintos para os três problemas definidos pelo procedimento de decomposição: convecção, difusão e pressão-velocidade. Um sistema hiperbólico de leis de conservação que modela o transporte convectivo das fases fluidas é aproximado por um esquema central de diferenças finitas explícito, conservativo, não oscilatório e de segunda ordem. Este esquema é combinado com elementos finitos mistos, localmente conservativos, para a aproximação numérica dos sistemas de equações parabólico e elíptico associados aos problemas de transporte difusivo e de pressão-velocidade, respectivamente. O operador temporal associado ao sistema parabólico é resolvido fazendo-se uso de uma estratégia implícita de solução (Backward Euler). O modelo matemático para escoamento trifásico considerado neste trabalho leva em conta as forças de capilaridade e expressões gerais para as funções de permeabilidade relativa, campos variáveis de porosidade e de permeabilidade e os efeitos da gravidade. A escolha de expressões gerais para as funções de permeabilidade relativa pode levar à perda de hiperbolicidade escrita e, desta maneira, à existência de uma região elíptica ou de pontos umbílicos para o sistema não linear de leis de conservação hiperbólicas que descreve o transporte convectivo das fases fluidas. Como consequência, a perda de hiperbolicidade pode levar à existência de choques não clássicos (também chamados de choques transicionais ou choques subcompressivos) nas soluções de escoamentos trifásicos. O novo procedimento numérico foi usado para investigar a existência e a estabilidade de choques não clássicos, com respeito ao fenômeno de fingering viscoso, em problemas de escoamentos trifásicos bidimensionais em reservatórios heterogêneos, estendendo deste modo resultados disponíveis na literatura para problemas de escoamentos trifásicos unidimensionais. Experimentos numéricos, incluindo o estudo de estratégias de injeção alternada de água e gás (Water-Alternating-Gas (WAG)), indicam que o novo procedimento numérico proposto conduz com eficiência computacional a resultados numéricos com precisão. Perspectivas para trabalhos de pesquisa futuros são também discutidas, tomando como base os desenvolvimentos reportados nesta tese.
We present a new, accurate fractional time-step method based on an operator splitting technique for the numerical solution of a system of partial differential equations modeling three-phase immiscible water-gas-oil flow problems in heterogeneous petroleum reservoirs in which the compressibility effects of the gas was not take into account. A two-level operator splitting technique allows for the use of distinct time steps for the three problems defined by the splitting procedure: convection, diffusion and pressure-velocity. A system of hyperbolic conservation laws modelling the convective transport of the fluid phases is approximated by a high resolution, nonoscillatory, second-order, conservative central difference scheme in the convection step. This scheme is combined with locally conservative mixed finite elements for the numerical solution of the parabolic and elliptic problems associated with the diffusive transport of fluid phases and the pressure-velocity problem, respectively. The time discretization of the parabolic problem is performed by means of the implicit backward Euler method. The mathematical model for the three-phase flow considered in this work takes into account capillary forces and general expressions for the relative permeability functions, variable porosity and permeability fields, and the effect of gravity. The choice of general expressions for the relative permeability functions may lead to the loss of strict hyperbolicity and, therefore, to the existence of an elliptic region of umbilic points for the systems of nonlinear hyperbolic conservation laws describing the convective transport of the fluid phases. As a consequence, the loss of hyperbolicity may lead to the existence of nonclassical shocks (also called transitional shocks or undercompressive shocks) in three-phase flow solutions. The numerical procedure was used in an investigation of the existence and stability of nonclassical shocks with respect to viscous fingering in heterogeneous two-dimensional flows, thereby extending previous results for one-dimensional three-phase flow available in the literature. Numerical experiments, including the study of Water-Alternating-Gas (WAG) injection strategies, indicate that the proposed new numerical procedure leads to computational efficiency and accurate numerical results. Directions for further research are also discussed, based on the developments reported in this thesis.

碩士
國立東華大學
材料科學與工程學系
101
In this study, we combine H2 evolution photocatalyst with O2 evolution photocatalyst, and use an aqueous NaI solution as I-/IO3- shuttle redox mediator in Z-scheme photocatalysis system for water splitting. We use solid state reaction to prepare H2 evolution photocatalyst, K4Nb6O17, and loading Rh as cocatalyst to improve hydrogen production. When the amount of loading Rh up to 1.5wt%, we get H2 evolution rate about 24mmol h-1 g-1 was higher than K4Nb6O17(337μmoleg-1h-1) as prepared. Then, we use exfoliation method to prepare our nanosheets photocatalyst, NS-K4Nb6O17, and loading Rh as cocatalyst, and exhibited a highest H2 evolution rate about 71 mmoleg-1h-1 when 1.5wt%Rh was loading. O2 evolution photocatalyst use WO3 loading 0.5wt%Pt as cocatalyst. The rate of H2 evolution and O2 evolution under UV irradiation significantly changed with the concentration of NaI, and the pH value of the reactant solution. The H2 and O2 production rate of K4Nb6O17/WO3-0.5wt%Pt Z-scheme photocatalysis system was 263μmol h-1 g-1 and 126μmol h-1 g-1, respectively. The optimal NaI concentration of the reactant solution 4mM at pH = 11. The H2 evolution and O2 evolution rate of K4Nb6O17/WO3-0.5wt%Pt Z-scheme photocatalysis system were enhanced by loading Rh nanoparticles as cocatalyst(H2:533μmoleg-1h-1，O2:259μmoleg-1h-1). The Z-scheme photocatalysis system with NS-K4Nb6O17 -1.5 wt%Rh/WO3-0.5wt%Pt photocatalysts exhibited a highest photoactivity with a H2 evolution rate of 1329μmol h-1 g-1 and a O2 evolution rate of 341μmol h-1 g-1.

碩士
國立臺灣大學
化學工程學研究所
97
The Z-scheme is a two-photocatalyst system for photocatalytic water splitting to produce hydrogen. The two-photocatalyst system is comprised of H2-catalyst and O2-catalyst to produce hydrogen and oxygen, respectively. Conventionally in Z-scheme, two catalysts are mixed in one reactor to perform photocatalytic water splitting, thus hydrogen and oxygen are produced as a mixture. Thus, the reverse reaction occurs to reduce the efficiency of water splitting. The cost of H2 separation is another drawback. Furthermore, a safety issue of H2-O2 explosion must be considered in the commercial process. This research used Pt/SrTiO3:Rh (H2-catalyst) and WO3 (O2-catalyst) discretely in two compartments of a connected twin reactor filled with aqueous solution. Two compartments of the twin reactor was separated by Nafion ion-exchanged membrane. Fe3+ and Fe2+ were added and served as electron-transfer mediates for redox reaction. The Nafion membrane was pretreated under Fe ion solution. The light source was 500W Halogen lamp. Under the visible-light irradiation, hydrogen and oxygen can be separately produced in two compartments simultaneously by photocatalytic water splitting. Under the optimal condition, the H2 yield reached 2.22 mole/g-h, and the molar ratio of H2/O2 was matched the stoichiometry of water splitting.

碩士
國立中央大學
資訊工程研究所
88
One way to broadcast a popular/hot video is to let multiple users share a few channels. The stress on the scarce channels can be alleviated without sacrificing viewer waiting time. One common approach is to partition the video into fixed-length segments, which are broadcast on several channels periodically. Two representative approaches are the Fast Broadcasting scheme and the PAGODA scheme , which can broadcast a video using k channels by having new-coming viewers to wait no longer than O(D/2^k) and O(D/5^(k/2)) time, respectively, where D is the length of the video. In this paper, we propose a new scheme, called Recursive Frequency-Splitting (RFS), that significantly improves over existing schemes in terms of viewer waiting time. Some lower bounds on the waiting time are also developed.

博士
國立臺灣大學
應用力學研究所
90
The relativistic kinetic flux vector splitting (KFVS) method is derived based on the special theory of relativity, the relativistic Boltzmann equation and the equilibrium, i.e., the Jüttner-Maxwell distribution function. The numerical first-order and the MUSCL-type second order schemes with van Leer limiters are developed in local rest frame and their counterparts in other inertial moving frames are obtained by Lorentz transformation, whose general transformation matrix is given in Appendix A and is formulated according to the one-dimensional Lorentz transformation in associated with the three-dimensional coordinate rotations. Both schemes are validated by the problems of one-dimensional Sod’s shock tube with different initial conditions and are applied to the two-dimensional spherical explosive waves. The intrinsic flaw of the original KFVS method is investigated. Due to the splitting of integration intervals for the distribution function, the propagation velocities of the macroscopic physical quantities are discrepant, which results in the breakdown of the conservation relations. The modified intervals of integration and the conditions for the KFVS method satisfying the conservation relations are proposed both for the classical and relativistic gas dynamics.

碩士
國立交通大學
材料科學與工程學系所
104
With the inherently high degree of complexity, semiconductor nanoheterostructures have exhibited superior synergistic properties that are difficult to acquire from their individual constituents. Particularly, great progress has been made in creating Z-scheme semiconductor-metal-semiconductor nanoheterostructures, in which the vectorial charge transfer scenario may increase the oxidizing and reducing powers for photoconversion applications. In this work, a ZnO nanorod-based Z-scheme nanoheterostrutcure system was proposed and realized for studying the photoelectrochemical properties in water splitting. The samples were prepared by selectively depositing a thin layer of SnO2 on the Au surface of Au nanoparticle-decorated ZnO nanorods using the photodeposition method. For Z-scheme ZnO-Au-SnO2 nanorods, the decorated Au may mediate interfacial charge transfer by promoting the electron transfer from the conduction band of SnO2 to the valence band of ZnO. This vectorial carrier transfer resulted in the situation that the photoexcited electrons accumulated at ZnO while the photogenerated holes remained at SnO2, rendering ZnO-Au-SnO2 sufficiently high redox powers. Time-resolved photoluminescence spectra and photovoltage analysis suggested that charge carrier separation was significantly improved in the ZnO-Au-SnO2 nanorods as a result of the Z-scheme charge transfer scenario. With the pronounced charge separation and sufficiently high redox powers, Z-scheme ZnO-Au-SnO2 nanorods performed much better in photoelectrochemical water splitting than pristine ZnO, two-component ZnO-Au and type-Ⅱ ZnO-SnO2 nanorods did. The demonstrations from this work may facilitate the use of Z-scheme nanoheterostructures in various photoconversion processes, in which the pronounced charge separation and high redox powers of Z-scheme charge transfer can be well employed.

碩士
國立東華大學
材料科學與工程學系
104
In this study , we use microwave–assisted to prepare O2 evolution photocatalyst, BiVO4. H2 evolution photocalyst use SSK4Nb6O17. The characterization of as-prepared BiVO4 was carried out by X-ray diffraction (XRD), Field Emission Scanning electron microscope (FE-SEM), ultraviolet-visible analyzer(UV-vis) and Surface Area & Mesopore Analyzer(BET) . In the process of photocatalyst synthesis, regulation of nitric acid concentration, temperature, and time as a different synthetic condition. Synthesis of time increases by the cubic morphology BiVO4 photocatalyst massive agglomeration into spherical structure and increasing the particle size. Synthesis of nitric acid concentration increased BiVO4 photocatalyst particles produced spherical agglomeration structure. Synthesis reaction temperature is increased to BiVO4 photocatalyst particle morphology little effect. With the synthesis reaction time stretched BiVO4 photocatalyst reduce the band gap. Synthesis of nitric acid concentration and temperature for BiVO4 photocatalyst band gap has little effect. Preparation impregnated with Pt/BiVO4 photocatalyst, Pt average particle size 17nm, evenly spread over the surface of the BiVO4 photocatalyst. Pt/BiVO4 photocatalyst was prepared by photodeposition method. Pt particles selectively deposited on {010} planes BiVO4 photocatalyst. Pt/BiVO4 photocatalyst optical absorption edge will move longer wavelength . Synthesis of nitric acid concentration increased, BiVO4 photocatalytic reaction rate decreases oxygen production. Synthesis of reaction temperature increases, BiVO4 photocatalytic reaction rate increased oxygen production. Synthesis of reaction temperature BiVO4 photocatalytic reaction rate on oxygen production is very important. The BiVO4(0.5M 180℃1hr) photocatalyst has the best photocatalytic reaction rate of oxygen production in AgNO3 aqueous solution. A O2 evolution rate of 2622 μmoleg-1h-1. Pt photodeposited BiVO4 photocatalyst was better than pure BiVO4 photocatalyst, the photocatalytic reaction rate of oxygen production was up 2 times in 5mM NaIO3 aqueous solution. Z-scheme system consist to hydrogen production catalyst (0.5wt%Rh/SSK4Nb6O17) and oxygen production catalyst(Pt/BiVO4). We found the Z-scheme photocatalysis system with 0.5wt%Pt-BiVO4-0.5wt%Rh/SSK4Nb6O17 photocatalysts exhibited a highest photoactivity with a H2 evolution rate of 348 μmole g-1 h-1 and a O2 evolution rate of 172 μmole g-1 h-1.

碩士
國立東華大學
材料科學與工程學系
101
The splitting of water into hydrogen and oxygen has been studied extensively, because of energy shortages in recent years. In the first part, this paper use the sol-gel and solid state sintering method to prepare potassium niobate (KNb3O8). We found the sol-gel method can use lower temperature to prepare potassium niobate(KNb3O8),and we can get higher hydrogen production activity. In the second part, we found potassium niobate (KNb3O8) has the highest bactericidal activity with 1wt% Ag by the photodeposition method. And the potassium niobate (KNb3O8) adds different amounts of Ag that can get different bactericidal activity. Final section, Z-scheme system consist to hydrogen production catalyst(KNb3O8)and oxygen production catalyst(BiVO4,WO3). I-/IO3- is redox mediator for Z-scheme system reaction. We found, different concentrations of NaI and PH value can affect the gas production activity.When 2mM concentration of NaI and PH value of 9 would have the best gas production activity in this paper. We found, the sol-gel method (KNb3O8) and commercial production of oxygen catalyst WO3 would have the best gas production activity in PH value of 9 (H2:538.72μmoleg-1h-1，O2:140.27μmoleg-1h-1) . Similarly we found the solid state sintering method (KNb3O8) and commercial production of oxygen catalyst WO3 would have the best gas production activity in PH value of 9. (H2:292.17μmoleg-1h-1，O2:130.83μmoleg-1h-1). Finally, we get the same result. The sol-gel method (KNb3O8) and BiVO4 would have the best gas production activity in PH value of 9. (H2:139.88μmoleg-1h-1，O2:49.5μmoleg-1h-1)

碩士
國立清華大學
通訊工程研究所
105
Incremental Redundancy Hybrid Automatic Repeat reQuest (IR-HARQ) is a popular scheme to achieve high throughput and be used in many communication systems. The rate-compatible codes are suitable for IR-HARQ and usually can be realized using puncturing, extension or splitting. However, all of them can not provide a satisfactory error performance over a wide range of code rates. In this thesis, the code construction scheme based on low density parity check (RC-LDPC) codes is proposed. In order to achieve a more flexible code construction over a wide range of code rates, the extension and splitting are combined in our design. The Approximate Cycle Extrinsic (ACE) message degree is also equiped to lower the error-floor, which is never considered in the previous RC-LDPC code construction scheme. The RC-LDPC codes from rate-4/5 to 1/3 which satisfactory error rate performance and low error-floor are demonstrated. In addition, the error-floor performance of the proposed RC-LDPC codes have been significiantly improved comparing to that the previous design using pure extension or splitting. In order to further improve the throughput, the incremental decoding is introduced and the decoding schedules are arranged by Maximum Mutual Information Increase ($M^2I^2$)-based algorithm. The system can achieve high throughput even if the number of iterations is limited.

碩士
國立東華大學
材料科學與工程學系
104
In this study, we used solid state reaction to prepare K4Nb6O17. Then, we used exfoliation method to prepare the nanosheets photocatalyst, NS-K4Nb6O17(NSK). Au, Rh, Graphite oxide(GO) were loaded to NSK as cocatalyst. The photocatalysis activity for H2 evolution in a Z-scheme on M/K4Nb6O17 (M= Au, Rh, GO) photocatalyst is studied. Pt/WO3 was used as O2 evolution photocatalyst. And NaI solution was used as shuttle redox mediator. The light source was a 400W medium-pressure Halogen lamp. The reaction of Z-scheme photocatalysis overall water splitting system was 43oC. The catalysts were characterized by X-ray diffraction(XRD), UV-visible, Gas Chromatography(GC), transmission electron microscopy(TEM), electrochemical analyzer. First, Au nanoparticle was prepared by using C6H5O7Na3 to reduce HAuCl4. Different amount of C6H5O7Na3 could prepare different size of Au nanoparticle,17 nm, 33 nm,40 nm . Au(m)/NSK with diameters of 33 nm Au nanoparticle had the best photoactivity (H2: 486 O2: 225 (μmol g-1 h-1)). Second, pyramid Rh nanoparticle was prepared by Na3RhCl6 reduced by L-ascorbic acid in triethylene glycol solution with PVP protector. By controlling concentration of Na3RhCl6, L-ascorbic acid and reaction time, different of size pyramid Rh nanoparticle,14 nm,25 nm,55 nm could be prepared. The highest of photoactivity H2 evolution photocatalyst is Rh(m)/NSK (H2: 759 O2: 415 (μmol g-1 h-1))with diameters of 25 nm pyramid Rh nanoparticle. The Rh/NSK photocatalyst was prepared by adding Na3RhCl6 to exfoliation solution of NSK. The Rh/NSK photocatalyst exhibited a vary high photoactivity (H2: 4240 O2: 1622 (μmol g-1 h-1)). Furthermore, GO was loading to Rh/NSK to improve photoactivity. The 3%GO/Rh/NSK photocatalyst was prepared by adding GO and Na3RhCl6 to exfoliation solution of NSK, and showed a higher photoactivity (H2: 5430 O2: 2226 (μmol g-1 h-1)). IMP-5%GO/Rh/NSK was prepared by Impregnation method showed the highest H2 evolution rate (H2: 7623 ) but O2 evolution rate was lower (O2: 1913 (μmol g-1 h-1)). The best way to load GO on NSK is to add GO in the NaI solution. A-5%GO/Rh/NSK exhibited a highest photoactivity (H2: 7039 O2: 3289 (μmol g-1 h-1)).

Least Square Kinetic Upwind Method (LSKUM) belongs to the class of mesh-less method that solves compressible Euler equations of gas dynamics. LSKUM is kinetic theory based upwind scheme that operates on any cloud of points. Euler equations are derived from Boltzmann equation (of kinetic theory of gases) after taking suitable moments. The basic update scheme is formulated at Boltzmann level and mapped to Euler level by suitable moments. Mesh-less solvers need only cloud of points to solve the governing equations. For a complex configuration, with such a solver, one can generate a separate cloud of points around each component, which adequately resolves the geometric features, and then combine all the individual clouds to get one set of points on which the solver directly operates. An obvious advantage of this approach is that any incremental changes in geometry will require only regeneration of the small cloud of points where changes have occurred. Additionally blanking and de-blanking strategy along with overlay point cloud can be adapted in some applications like store separation to avoid regeneration of points. Naturally, the mesh-less solvers have advantage in tackling complex geometries and moving components over solvers that need grids. Conventionally, higher order accuracy for space derivative term is achieved by two step defect correction formula which is computationally expensive. The present solver uses low dissipation single step modified CIR (MCIR) scheme which is similar to first order LSKUM formulation and provides spatial accuracy closer to second order. The maximum time step taken to march solution in time is limited by stability criteria in case of explicit time integration procedure. Because of this, explicit scheme takes a large number of iterations to achieve convergence. The popular explicit time integration schemes like four stages Runge-Kutta (RK4) are slow in convergence due to this reason. The above problem can be overcome by using the implicit time integration procedure. The implicit schemes are unconditionally stable i.e. very large time steps can be used to accelerate the convergence. Also it offers superior robustness. The implicit Lower-Upper Symmetric Gauss-Seidel (LU-SGS) scheme is very attractive due to its low numerical complexity, moderate memory requirement and unconditional stability for linear wave equation. Also this scheme is more efficient than explicit counterparts and can be implemented easily on parallel computers. It is based on the factorization of the implicit operator into three parts namely lower triangular matrix, upper triangular matrix and diagonal terms. The use of LU-SGS results in a matrix free implicit framework which is very economical as against other expensive procedures which necessarily involve matrix inversion. With implementation of the implicit LU-SGS scheme larger time steps can be used which in turn will reduce the computational time substantially. LU-SGS has been used widely for many Finite Volume Method based solvers. The split flux Jacobian formulation as proposed by Jameson is most widely used to make implicit procedure diagonally dominant. But this procedure when applied to mesh-less solvers leads to block diagonal matrix which again requires expensive inversion. In the present work LU-SGS procedure is adopted for mesh-less approach to retain diagonal dominancy and implemented in 2-D and 3-D solvers in matrix free framework. In order to assess the efficacy of the implicit procedure, both explicit and implicit 2-D solvers are tested on NACA 0012 airfoil for various flow conditions in subsonic and transonic regime. To study the performance of the solvers on different point distributions two types of the cloud of points, one unstructured distribution (4074 points) and another structured distribution (9600 points) have been used. The computed 2-D results are validated against NASA experimental data and AGARD test case. The density residual and lift coefficient convergence history is presented in detail. The maximum speed up obtained by use of implicit procedure as compared to explicit one is close to 6 and 14 for unstructured and structured point distributions respectively. The transonic flow over ONERA M6 wing is a classic test case for CFD validation because of simple geometry and complex flow. It has sweep angle of 30° and 15.6° at leading edge and trailing edge respectively. The taper ratio and aspect ratio of the wing are 0.562 and 3.8 respectively. At M∞=0.84 and α=3.06° lambda shock appear on the upper surface of the wing. 3¬D explicit and implicit solvers are tested on ONERA M6 wing. The computed pressure coefficients are compared with experiments at section of 20%, 44%, 65%, 80%, 90% and 95% of span length. The computed results are found to match very well with experiments. The speed up obtained from implicit procedure is over 7 for ONERA M6 wing. The determination of the aerodynamic characteristics of a wing with the control surface deflection is one of the most important and challenging task in aircraft design and development. Many military aircraft use some form of the delta wing. To demonstrate the effectiveness of 3-D solver in handling control surfaces and small gaps, implicit 3-D code is used to compute flow past clipped delta wing with aileron deflection of 6° at M∞ = 0.9 and α = 1° and 3°. The leading edge backward sweep is 50.4°. The aileron is hinged from 56.5% semi-span to 82.9% of semi-span and at 80% of the local chord from leading edge. The computed results are validated with NASA experiments

Least Square Kinetic Upwind Method (LSKUM) belongs to the class of mesh-less method that solves compressible Euler equations of gas dynamics. LSKUM is kinetic theory based upwind scheme that operates on any cloud of points. Euler equations are derived from Boltzmann equation (of kinetic theory of gases) after taking suitable moments. The basic update scheme is formulated at Boltzmann level and mapped to Euler level by suitable moments. Mesh-less solvers need only cloud of points to solve the governing equations. For a complex configuration, with such a solver, one can generate a separate cloud of points around each component, which adequately resolves the geometric features, and then combine all the individual clouds to get one set of points on which the solver directly operates. An obvious advantage of this approach is that any incremental changes in geometry will require only regeneration of the small cloud of points where changes have occurred. Additionally blanking and de-blanking strategy along with overlay point cloud can be adapted in some applications like store separation to avoid regeneration of points. Naturally, the mesh-less solvers have advantage in tackling complex geometries and moving components over solvers that need grids. Conventionally, higher order accuracy for space derivative term is achieved by two step defect correction formula which is computationally expensive. The present solver uses low dissipation single step modified CIR (MCIR) scheme which is similar to first order LSKUM formulation and provides spatial accuracy closer to second order. The maximum time step taken to march solution in time is limited by stability criteria in case of explicit time integration procedure. Because of this, explicit scheme takes a large number of iterations to achieve convergence. The popular explicit time integration schemes like four stages Runge-Kutta (RK4) are slow in convergence due to this reason. The above problem can be overcome by using the implicit time integration procedure. The implicit schemes are unconditionally stable i.e. very large time steps can be used to accelerate the convergence. Also it offers superior robustness. The implicit Lower-Upper Symmetric Gauss-Seidel (LU-SGS) scheme is very attractive due to its low numerical complexity, moderate memory requirement and unconditional stability for linear wave equation. Also this scheme is more efficient than explicit counterparts and can be implemented easily on parallel computers. It is based on the factorization of the implicit operator into three parts namely lower triangular matrix, upper triangular matrix and diagonal terms. The use of LU-SGS results in a matrix free implicit framework which is very economical as against other expensive procedures which necessarily involve matrix inversion. With implementation of the implicit LU-SGS scheme larger time steps can be used which in turn will reduce the computational time substantially. LU-SGS has been used widely for many Finite Volume Method based solvers. The split flux Jacobian formulation as proposed by Jameson is most widely used to make implicit procedure diagonally dominant. But this procedure when applied to mesh-less solvers leads to block diagonal matrix which again requires expensive inversion. In the present work LU-SGS procedure is adopted for mesh-less approach to retain diagonal dominancy and implemented in 2-D and 3-D solvers in matrix free framework. In order to assess the efficacy of the implicit procedure, both explicit and implicit 2-D solvers are tested on NACA 0012 airfoil for various flow conditions in subsonic and transonic regime. To study the performance of the solvers on different point distributions two types of the cloud of points, one unstructured distribution (4074 points) and another structured distribution (9600 points) have been used. The computed 2-D results are validated against NASA experimental data and AGARD test case. The density residual and lift coefficient convergence history is presented in detail. The maximum speed up obtained by use of implicit procedure as compared to explicit one is close to 6 and 14 for unstructured and structured point distributions respectively. The transonic flow over ONERA M6 wing is a classic test case for CFD validation because of simple geometry and complex flow. It has sweep angle of 30° and 15.6° at leading edge and trailing edge respectively. The taper ratio and aspect ratio of the wing are 0.562 and 3.8 respectively. At M∞=0.84 and α=3.06° lambda shock appear on the upper surface of the wing. 3¬D explicit and implicit solvers are tested on ONERA M6 wing. The computed pressure coefficients are compared with experiments at section of 20%, 44%, 65%, 80%, 90% and 95% of span length. The computed results are found to match very well with experiments. The speed up obtained from implicit procedure is over 7 for ONERA M6 wing. The determination of the aerodynamic characteristics of a wing with the control surface deflection is one of the most important and challenging task in aircraft design and development. Many military aircraft use some form of the delta wing. To demonstrate the effectiveness of 3-D solver in handling control surfaces and small gaps, implicit 3-D code is used to compute flow past clipped delta wing with aileron deflection of 6° at M∞ = 0.9 and α = 1° and 3°. The leading edge backward sweep is 50.4°. The aileron is hinged from 56.5% semi-span to 82.9% of semi-span and at 80% of the local chord from leading edge. The computed results are validated with NASA experiments

碩士
中原大學
數學研究所
86
In this paper，the ENO schemes with Marquina‘s fluxsplitting are implemented and tested. When traditionalmethods like Godunov method and Harten’s TVD scheme are used to compute the test problems chosen below，ncorrect features like postshock osillations andspikes in the density and momentum profile appear inthe numerical solutions。ENO schemes with Marquina‘sflux splitting are able to provided more acceptablenumerical approximations in these situations withoutusing any problem dependent fixes and thus provided amore robust family of characteristic based method。

Time splitting is a numerical procedure used in solution of partial differential equations whose solutions allow multiple time scales. Numerical schemes are split for handling the stiffness in equations, i.e. when there are multiple time scales with a few time scales being smaller than the others. When there are such terms with smaller time scales, due to the Courant number restriction, the computational cost becomes high if these terms are treated explicitly. In the present work a nonlinear advective equation is solved numerically using different techniques based on a generalised framework for splitting methods. The nonlinear advective equation was chosen because it has an analytical solution making comparisons with numerical schemes amenable and also because its nonlinearity mimics the equations encountered in atmospheric modelling. Using the nonlinear advective equation as a test bed, an analysis of the splitting methods and their influence on the split solutions has been made. An understanding of influence of splitting schemes requires knowledge of behaviour of unsplit schemes beforehand. Hence a study on unsplit methods has also been made. In the present work, using the nonlinear advective equation, it shown that the three time level schemes have high phase errors and underestimate energy (even though they have a higher order of accuracy in time). It is also found that the leap-frog method, which is used widely in atmospheric modelling, is the worst among examined unsplit methods. The semi implicit method, again a popular splitting method with atmospheric modellers is the worst among examined split methods. Three time-level schemes also need explicit filtering to remove the computational mode. This filtering can have a significant impact on the obtained numerical solutions, and hence three-time level schemes appear to be unattractive in the context of the nonlinear convective equation. Based on this experience, splitting methods for the two-time level schemes is proposed. These schemes realistically capture the phase and energy of the nonlinear advective equation.

Time splitting is a numerical procedure used in solution of partial differential equations whose solutions allow multiple time scales. Numerical schemes are split for handling the stiffness in equations, i.e. when there are multiple time scales with a few time scales being smaller than the others. When there are such terms with smaller time scales, due to the Courant number restriction, the computational cost becomes high if these terms are treated explicitly. In the present work a nonlinear advective equation is solved numerically using different techniques based on a generalised framework for splitting methods. The nonlinear advective equation was chosen because it has an analytical solution making comparisons with numerical schemes amenable and also because its nonlinearity mimics the equations encountered in atmospheric modelling. Using the nonlinear advective equation as a test bed, an analysis of the splitting methods and their influence on the split solutions has been made. An understanding of influence of splitting schemes requires knowledge of behaviour of unsplit schemes beforehand. Hence a study on unsplit methods has also been made. In the present work, using the nonlinear advective equation, it shown that the three time level schemes have high phase errors and underestimate energy (even though they have a higher order of accuracy in time). It is also found that the leap-frog method, which is used widely in atmospheric modelling, is the worst among examined unsplit methods. The semi implicit method, again a popular splitting method with atmospheric modellers is the worst among examined split methods. Three time-level schemes also need explicit filtering to remove the computational mode. This filtering can have a significant impact on the obtained numerical solutions, and hence three-time level schemes appear to be unattractive in the context of the nonlinear convective equation. Based on this experience, splitting methods for the two-time level schemes is proposed. These schemes realistically capture the phase and energy of the nonlinear advective equation.

Efficient implementation of resource sharing strategies in a multi-user wireless environment can improve the performance of a network significantly. In this thesis we study various scheduling strategies for wireless networks and handle the problem of opportunistically scheduling transmissions using channel aware schemes. First we propose a scheme that can handle users with asymmetric channel conditions and is opportunistic in the sense that it exploits the multi-user diversity of the network. The scheme requires the users to have a priori knowledge of their channel distributions. The associated overhead is limited meaning it offers reduced feedback load, that does not scale with the increasing number of users. The main technique used to shrink the feedback load is the contention based distributed implementation of a splitting algorithm that does not require explicit feedback to the scheduler from every user. The users find the best among themselves, in a distributed manner, while requiring just a ternary broadcast feedback from the scheduler at the end of each mini-slot. In addition, it can also handle fairness constraints in time and throughput to various degrees. Next we propose another opportunistic scheduler that offers most of the benefits of the previously proposed scheme but is more practical because it can also handle heterogenous users whose channel distributions are unknown. This new scheme actually reduces the complexity and is also more robust for changing traffic patterns. Finally we extend both these schemes to the scenario where there are fixed thresholds, this enables us to handle opportunistic scheduling in practical systems that can only transmit over finite number of discrete rates with the additional benefit that full feedback session, even from the selected user, is never required.

博士
國立臺灣大學
土木工程學研究所
92
The development of a numerical scheme that resolves sharp discontinuities without spurious oscillations and do not produce too much numerical dissipation is of great importance in the computational shallow-water hydrodynamics. In this thesis, three hybrid flux-splitting finite-volume schemes are proposed for solving two-dimensional shallow water equations. In the framework of the finite volume method, a hybrid flux-splitting algorithm without Jacobian matrix operation is established by applying the advection upstream splitting method (AUSM) to estimate the cell-interface fluxes. Based on the proposed algorithm, a first-order hybrid flux-splitting finite-volume (HFS) scheme is developed, which is robust and rather simple to implement. To improve the numerical resolutions of discontinuities, the monotonic upstream schemes for conservation laws (MUSCL) method with limiters and the two-step component-wise total variation diminishing (TVD) method are adopted for the second-order extensions. The proposed three finite-volume schemes are verified through the simulations of the 1D idealized dam-break, extreme rarefaction wave, steady transcritical flow and oblique hydraulic jump problems. The numerical results by the proposed schemes are compared with those by other shock-capturing upwind schemes as well as exact solutions. It is demonstrated that the proposed schemes are accurate and efficient to capture the discontinuous solutions without any spurious oscillations in the complex flow domains with dry-bed situation, bottom slope or friction. In addition, the proposed schemes are proven to produce no entropy-violating solution and to achieve the benefits combining the efficiency of flux-vector splitting (FVS) scheme and the accuracy of flux-difference splitting (FDS) scheme. Furthermore, the proposed schemes are applied to simulate several 2D dam-break problems, including the partial dam breaking, circular dam breaking and four experimental dam-break problems. The simulated results show that the proposed schemes can deal with the rarefaction waves, shocks, the reflected shocks, the reverse flows and the dry/wet fronts very well.