Dissertations / Theses: 'Numerical scheme for SDEs'

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Kumar, Chaman. "Explicit numerical schemes of SDEs driven by Lévy noise with super-linear coeffcients and their application to delay equations." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/15946.

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We investigate an explicit tamed Euler scheme of stochastic differential equation with random coefficients driven by Lévy noise, which has super-linear drift coefficient. The strong convergence property of the tamed Euler scheme is proved when drift coefficient satisfies one-sided local Lipschitz condition whereas diffusion and jump coefficients satisfy local Lipschitz conditions. A rate of convergence for the tamed Euler scheme is recovered when local Lipschitz conditions are replaced by global Lipschitz conditions and drift satisfies polynomial Lipschitz condition. These findings are consistent with those of the classical Euler scheme. New methodologies are developed to overcome challenges arising due to the jumps and the randomness of the coefficients. Moreover, as an application of these findings, a tamed Euler scheme is proposed for the stochastic delay differential equation driven by Lévy noise with drift coefficient that grows super-linearly in both delay and non-delay variables. The strong convergence property of the tamed Euler scheme for such SDDE driven by Lévy noise is studied and rate of convergence is shown to be consistent with that of the classical Euler scheme. Finally, an explicit tamed Milstein scheme with rate of convergence arbitrarily close to one is developed to approximate the stochastic differential equation driven by Lévy noise (without random coefficients) that has super-linearly growing drift coefficient.

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Alnafisah, Yousef Ali. "First-order numerical schemes for stochastic differential equations using coupling." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/20420.

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We study a new method for the strong approximate solution of stochastic differential equations using coupling and we prove order one error bounds for the new scheme in Lp space assuming the invertibility of the diffusion matrix. We introduce and implement two couplings called the exact and approximate coupling for this scheme obtaining good agreement with the theoretical bound. Also we describe a method for non-invertibility case (Combined method) and we investigate its convergence order which will give O(h3/4 √log(h)j) under some conditions. Moreover we compare the computational results for the combined method with its theoretical error bound and we have obtained a good agreement between them. In the last part of this thesis we work out the performance of the multilevel Monte Carlo method using the new scheme with the exact coupling and we compare the results with the trivial coupling for the same scheme.

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Handari, Bevina D. "Numerical methods for SDEs and their dynamics /." [St. Lucia, Qld.], 2002. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe17145.pdf.

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Tzitzili, Efthalia. "Numerical approximation of Stratonovich SDEs and SPDEs." Thesis, Heriot-Watt University, 2015. http://hdl.handle.net/10399/2883.

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We consider the numerical approximation of stochastic differential and partial differential equations S(P)DEs, by means of time-differencing schemes which are based on exponential integrator techniques. We focus on the study of two numerical schemes, both appropriate for the simulation of Stratonovich- interpreted S(P)DEs. The first, is a basic strong order 1=2 scheme, called Stratonovich Exponential Integrators (SEI). Motivated by SEI and aiming at benefiting both from the higher order of the standard Milstein scheme and the efficiency of the exponential schemes when dealing with stiff problems, we develop a new Milstein type scheme called Milstein Stratonovich Exponential Integrators (MSEI). We prove strong convergence of the SEI scheme for high-dimensional semilinear Stratonovich SDEs with multiplicative noise and we use SEI as well as the MSEI scheme to approximate solutions of the stochastic Landau-Lifschitz- Gilbert (LLG) equation in three dimensions. We examine the L2(Ω ) approximation error of the SEI and MSEI schemes numerically and we prove analytically that MSEI achieves a higher order of convergence than SEI. We generalise SEI so that it is suited not only for Stratonovich SDEs, but also for It^o and for SDEs interpreted by the 'in-between' calculi. Moreover, we provide a general expression for the predictor contained in SEI and we study the theoretical convergence for the generalised version of the scheme. We show that the order of the scheme used in order to obtain the predictor as well as the stochastic integral interpretation do not affect the overall order of the scheme. We extend the convergence results for SEI to a space-time context by considering a second order semilinear Stratonovich SPDE with multiplicative noise. We discretise in space with the nite element method and we use SEI for discretising in time. We consider the case where we have trace class noise and we examine analytically the strong order of convergence for SEI. We implement SEI as a time discretisation scheme and present the results when simulating SPDEs with stochastic travelling wave solutions. Then, we use an alternative method, called 'freezing' method, for approximating wave solutions and estimating the speed of the waves for the stochastic Nagumo and FitzHugh-Nagumo models. The wave position and hence the speed is found by minimising the L2 distance between a reference function and the travelling wave. While the results obtained from the two different approaches agree, we observe that the behaviour of the wave solution is captured in a smaller computational domain, when we use the freezing method, making it more efficient for long time simulations.

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Campana, Lorenzo. "Modélisation stochastique de particules non sphériques en turbulence." Thesis, Université Côte d'Azur, 2022. http://www.theses.fr/2022COAZ4019.

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Le mouvement de petites particules non-sphériques en suspension dans un écoulement turbulent a lieu dans une grande variété d’applications naturelles et industrielles. Par exemple, ces phénomènes impactent la dynamique des aérosols dans l’atmosphère et dans les voies respiratoires, le mouvement des globules rouges dans le sang, la dynamique du plancton dans l’océan, la glace dans les nuages ou bien la combustion. Les particules anisotropes réagissent aux écoulements turbulents de manière complexe. Leur dynamique dépend ainsi d’un large éventail de para- mètres (forme, inertie, cisaillement du fluide). Les particules sans inertie, dont la taille est inférieure à la longueur de Kolmogorov, suivent le mouvement du fluide avec une orientation généralement gouvernée par le gradient local de vitesse turbulente. Cette thèse est axée sur la dynamique de tels objets en turbulence en ayant recours à des méthodes Lagrangienes stochastiques. Le développement d’un modèle qui peut être utilisé comme outil prédictif dans le cadre de la dynamique de fluides numérique (CFD) au niveau industriel est d’un grand intérêt pour les applications concrètes en ingénierie. Par ailleurs, pour progresser dans le domaine de la médecine, de l’environnement et des procédés industriels, il est nécessaire que ces modèles atteignent un compromis acceptable entre simplicité et précision. La formulation d’un modèle stochastique pour l’orientation de telles particules est tout d’abord présentée dans le cadre d’un écoulement turbulent bidimensionnel avec un cisaillement homogène. Des simulations numériques directes (DNS) sont produites pour guider et évaluer la proposition de modèle. Les questions abordés dans ce travail portent sur la représentation de formes analytiques du modèle, sur les effets des anisotropies inclues dans le modèle, et sur l’extension de la notion de dynamique rotationnelle dans le cadre de cette approche stochastique. Les résultats obtenus avec le modèle, comparés avec la DNS, produisent une réponse qualitative acceptable, même si ce modèle diffusif n’est pas conçu pour reproduire les caractéristiques non-gaussiennes des expériences numériques (DNS). L’extension au cas tridimensionnel du modèle d’orientation pose le problème de son implé- mentation numérique efficace. Dans ce travail, un schéma numérique capable de simuler la dynamique d’orientation de telles particules, à un coût de calcul raisonnable, est introduit. La convergence de ce schéma est également analysée. Pour ce faire, un schéma fondé sur la décomposition de la dynamique a été développé pour résoudre les équations différen- tielles stochastiques (EDS) de rotation de ces particules. Cette décomposition permet de surmonter les problèmes d’instabilité typiques de la méthode Euler–Maruyama; on a ainsi obtenu une convergence en norme L2 d’ordre 1/2 et une convergence faible d’ordre 1, comme classiquement attendu. Enfin, le schéma numérique a été implémenté dans un code CFD industriel (Code_Saturne). Ce modèle a ensuite été utilisé pour étudier l’orientation et la rotation de particules anisotropes sans inertie dans le cas d’un écoulement turbulent inhomogène, à savoir un écoulement de canal plan turbulent. Cette application dans un cas pratique a permis de mettre en evidence deux difficultés liées au modèle : d’abord, l’implémentation numérique dans un code industriel, ensuite la capacité du modèle à reproduire les expériences numériques obtenues par DNS. Ainsi, le modèle stochastique Lagrangien pour l’orientation de sphéroïdes implémenté dans Code_Saturne permet de reproduire, avec certaines limites, les statistiques d’orientation et de rotation de sphéroïdes mesurées dans la DNS
The motion of small non- spherical particles suspended in a turbulent flow is relevant for a large variety of natural and industrial applications such as aerosol dynamics in respiration, red blood cells motion, plankton dynamics, ice in clouds, combustion, to name a few. Anisotropic particles react on turbulent flows in complex ways, which depend on a wide range of parameters (shape, inertia, fluid shear). Inertia-free particles, with size smaller than the Kolmogorov length, follow the fluid motion with an orientation generally defined by the local turbulent velocity gradient. Therefore, this thesis is focused on the dynamics of these objects in turbulence exploiting stochastic Lagrangian methods. The development of a model that can be used as predictive tool in industrial computational fluid dynamics (CFD) is highly valuable for practical applications in engineering. Models that reach an acceptable compromise between simplicity and accuracy are needed for progressing in the field of medical, environmental and industrial processes. The formulation of a stochastic orientation model is studied in two-dimensional turbulent flow with homogeneous shear, where results are compared with direct numerical simulations (DNS). Finding analytical results, scrutinising the effect of the anisotropies when they are included in the model, and extending the notion of rotational dynamics in the stochastic framework, are subjects addressed in our work. Analytical results give a reasonable qualitative response, even if the diffusion model is not designed to reproduce the non-Gaussian features of the DNS experiments. The extension to the three-dimensional case showed that the implementation of efficient numerical schemes in 3D models is far from straightforward. The introduction of a numerical scheme with the capability to preserve the dynamics at reasonable computational costs has been devised and the convergence analysed. A scheme of splitting decomposition of the stochastic differential equations (SDE) has been developed to overcome the typical instability problems of the Euler–Maruyama method, obtaining a mean-square convergence of order 1/2 and a weakly convergence of order 1, as expected. Finally, model and numerical scheme have been implemented in an industrial CFD code (Code_Saturne) and used to study the orientational and rotational behaviour of anisotropic inertia-free particles in an applicative prototype of inhomogeneous turbulence, i.e. a turbulent channel flow. This real application has faced two issues of the modelling: the numerical implementation in an industrial code, and whether and to which extent the model is able to reproduce the DNS experiments. The stochastic Lagrangian model for the orientation in the CFD code reproduces with some limits the orientation and rotation statistics of the DNS. The results of this study allows to predict the orientation and rotation of aspherical particles, giving new insight into the prediction of large scale motions both, in two-dimensional space, of interest for geophysical flows, and in three-dimensional industrial applications

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Herdiana, Ratna. "Numerical methods for SDEs - with variable stepsize implementation /." [St. Lucia, Qld.], 2003. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe17638.pdf.

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Yannios, Nicholas, and mikewood@deakin edu au. "Computational aspects of the numerical solution of SDEs." Deakin University. School of Computing and Mathematics, 2001. http://tux.lib.deakin.edu.au./adt-VDU/public/adt-VDU20060817.123449.

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In the last 30 to 40 years, many researchers have combined to build the knowledge base of theory and solution techniques that can be applied to the case of differential equations which include the effects of noise. This class of ``noisy'' differential equations is now known as stochastic differential equations (SDEs). Markov diffusion processes are included within the field of SDEs through the drift and diffusion components of the Itô form of an SDE. When these drift and diffusion components are moderately smooth functions, then the processes' transition probability densities satisfy the Fokker-Planck-Kolmogorov (FPK) equation -- an ordinary partial differential equation (PDE). Thus there is a mathematical inter-relationship that allows solutions of SDEs to be determined from the solution of a noise free differential equation which has been extensively studied since the 1920s. The main numerical solution technique employed to solve the FPK equation is the classical Finite Element Method (FEM). The FEM is of particular importance to engineers when used to solve FPK systems that describe noisy oscillators. The FEM is a powerful tool but is limited in that it is cumbersome when applied to multidimensional systems and can lead to large and complex matrix systems with their inherent solution and storage problems. I show in this thesis that the stochastic Taylor series (TS) based time discretisation approach to the solution of SDEs is an efficient and accurate technique that provides transition and steady state solutions to the associated FPK equation. The TS approach to the solution of SDEs has certain advantages over the classical techniques. These advantages include their ability to effectively tackle stiff systems, their simplicity of derivation and their ease of implementation and re-use. Unlike the FEM approach, which is difficult to apply in even only two dimensions, the simplicity of the TS approach is independant of the dimension of the system under investigation. Their main disadvantage, that of requiring a large number of simulations and the associated CPU requirements, is countered by their underlying structure which makes them perfectly suited for use on the now prevalent parallel or distributed processing systems. In summary, l will compare the TS solution of SDEs to the solution of the associated FPK equations using the classical FEM technique. One, two and three dimensional FPK systems that describe noisy oscillators have been chosen for the analysis. As higher dimensional FPK systems are rarely mentioned in the literature, the TS approach will be extended to essentially infinite dimensional systems through the solution of stochastic PDEs. In making these comparisons, the advantages of modern computing tools such as computer algebra systems and simulation software, when used as an adjunct to the solution of SDEs or their associated FPK equations, are demonstrated.

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Adamu, Iyabo Ann. "Numerical approximation of SDEs and stochastic Swift-Hohenberg equation." Thesis, Heriot-Watt University, 2011. http://hdl.handle.net/10399/2460.

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We consider the numerical approximation of stochastic differential equations interpreted both in the It^o and Stratonovich sense and develop three stochastic time-integration techniques based on the deterministic exponential time differencing schemes. Two of the numerical schemes are suited for the simulations of It^o stochastic ordinary differential equations (SODEs) and they are referred to as the stochastic exponential time differencing schemes, SETD0 and SETD1. The third numerical scheme is a new numerical method we propose for the simulations of Stratonovich SODEs. We call this scheme, the Exponential Stratonovich Integrator (ESI). We investigate numerically the convergence of these three numerical methods, in addition to three standard approximation schemes and also compare the accuracy and efficiency of these schemes. The effect of small noise is also studied. We study the theoretical convergence of the stochastic exponential time differencing scheme (SETD0) for parabolic stochastic partial differential equations (SPDEs) with infinite-dimensional additive noise and one-dimensional multiplicative noise. We obtain a strong error temporal estimate of O(¢tµ + ²¢tµ + ²2¢t1=2) for SPDEs forced with a one-dimensional multiplicative noise and also obtain a strong error temporal estimate of O(¢tµ + ²2¢t) for SPDEs forced with an infinite-dimensional additive noise. We examine convergence for second-order and fourth-order SPDEs. We consider the effects of spatially correlated and uncorrelated noise on bifurcations for SPDEs. In particular, we study a fourth-order SPDE, the Swift-Hohenberg equation, and allow the control parameter to fluctuate. Numerical simulations show a shift in the pinning region with multiplicative noise.

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Gil, Gibin. "Hybrid Numerical Integration Scheme for Highly Oscillatory Dynamical Systems." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/306771.

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Computational efficiency of solving the dynamics of highly oscillatory systems is an important issue due to the requirement of small step size of explicit numerical integration algorithms. A system is considered to be highly oscillatory if it contains a fast solution that varies regularly about a slow solution. As for multibody systems, stiff force elements and contacts between bodies can make a system highly oscillatory. Standard explicit numerical integration methods should take a very small step size to satisfy the absolute stability condition for all eigenvalues of the system and the computational cost is dictated by the fast solution. In this research, a new hybrid integration scheme is proposed, in which the local linearization method is combined with a conventional integration method such as the fourth-order Runge-Kutta. In this approach, the system is partitioned into fast and slow subsystems. Then, the two subsystems are transformed into a reduced and a boundary-layer system using the singular perturbation theory. The reduced system is solved by the fourth-order Runge-Kutta method while the boundary-layer system is solved by the local linearization method. This new hybrid scheme can handle the coupling between the fast and the slow subsystems efficiently. Unlike other multi-rate or multi-method schemes, extrapolation or interpolation process is not required to deal with the coupling between subsystems. Most of the coupling effect can be accounted for by the reduced (or quasi-steady-state) system while the minor transient effect is taken into consideration by averaging. In this research, the absolute stability region for this hybrid scheme is derived and it is shown that the absolute stability region is almost independent of the fast variables. Thus, the selection of the step size is not dictated by the fast solution when a highly oscillatory system is solved, in turn, the computational efficiency can be improved. The advantage of the proposed hybrid scheme is validated through several dynamic simulations of a vehicle system including a flexible tire model. The results reveal that the hybrid scheme can reduce the computation time of the vehicle dynamic simulation significantly while attaining comparable accuracy.

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Alhojilan, Yazid Yousef M. "Higher-order numerical scheme for solving stochastic differential equations." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/15973.

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We present a new pathwise approximation method for stochastic differential equations driven by Brownian motion which does not require simulation of the stochastic integrals. The method is developed to give Wasserstein bounds O(h3/2) and O(h2) which are better than the Euler and Milstein strong error rates O(√h) and O(h) respectively, where h is the step-size. It assumes nondegeneracy of the diffusion matrix. We have used the Taylor expansion but generate an approximation to the expansion as a whole rather than generating individual terms. We replace the iterated stochastic integrals in the method by random variables with the same moments conditional on the linear term. We use a version of perturbation method and a technique from optimal transport theory to find a coupling which gives a good approximation in Lp sense. This new method is a Runge-Kutta method or so-called derivative-free method. We have implemented this new method in MATLAB. The performance of the method has been studied for degenerate matrices. We have given the details of proof for order h3/2 and the outline of the proof for order h2.

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Brown, Sarah M. "A numerical scheme for Mullins-Sekerka flow in three space dimensions /." Diss., CLICK HERE for online access, 2004. http://contentdm.lib.byu.edu/ETD/image/etd493.pdf.

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Brown, Sarah Marie. "A Numerical Scheme for Mullins-Sekerka Flow in Three Space Dimensions." BYU ScholarsArchive, 2004. https://scholarsarchive.byu.edu/etd/136.

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The Mullins-Sekerka problem, also called two-sided Hele-Shaw flow, arises in modeling a binary material with two stable concentration phases. A coarsening process occurs, and large particles grow while smaller particles eventually dissolve. Single particles become spherical. This process is described by evolving harmonic functions within the two phases with the moving interface driven by the jump in the normal derivatives of the harmonic functions at the interface. The harmonic functions are continuous across the interface, taking on values equal to the mean curvature of the interface. This dissertation reformulates the three-dimensional problem as one on the two-dimensional interface by using boundary integrals. A semi-implicit scheme to solve the free boundary problem numerically is implemented. Numerical analysis tasks include discretizing surfaces, overcoming node bunching, and dealing with topology change in a toroidal particle. A particle (node)-cluster technique is developed with the aim of alleviating excessive run time caused by filling the dense matrix used in solving a system of linear equations.

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Miri, Seyedalireza. "Numerical Solution of Moment Equations Using the Discontinuous-Galerkin Hancock Method." Thesis, Université d'Ottawa / University of Ottawa, 2019. http://hdl.handle.net/10393/38678.

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Moment methods from the kinetic theory of gases exist as an alternative to the Navier-Stokes model. Models in this family are described by first-order hyperbolic PDEs with local relaxation. They provide a natural treatment for non-equilibrium effects and expand the regime for which the model is physically applicable past the Navier-Stokes level (when the continuum assumption breaks down). Discontinuous-Galerkin (DG) methods are very well suited for distributed parallel solution of first-order PDEs. This is because the optimal locality of the method minimizes needed communication between computational processes. One highly efficient, coupled space-time DG method that achieves third-order accuracy in both space and time while using only linear elements is the discontinuous-Galerkin Hancock (DGH) scheme, which was specifically designed for the efficient solution of PDEs resulting from moment closures. Third-order accuracy is obtained through the use of a technique originally proposed by Hancock. The combination of moment methods with the DGH discretization leads to a very efficient numerical treatment for viscous compressible gas flows that is accurate both in and out of local thermodynamic equilibrium. This thesis describe the first-ever implementation of this scheme for the solution of moment equations on large-scale distributed-memory computers. This implementation uses solution-directed automatic mesh refinement to increase accuracy while reducing cost. A linear hyperbolic-relaxation equation is used to verify the order of accuracy of the scheme. Next a supersonic compressible Euler case is used to demonstrate the mesh refinement as well as the scheme’s ability to capture sharp discontinuities. Third, a moment-closure is then used to compute a viscous mixing layer. This serves to demonstrate the ability of the first-order PDEs and the DG scheme to efficiently compute viscous solutions. A moment-closure is used to compute the solution for Stokes flow past a circular cylinder. This case reinforces the hyperbolic PDEs’ ability to accurately predict viscous phenomena. As this case is very low speed, it also demonstrates the numerical technique’s ability to accurately solve problems that are ill-conditioned due to the extremely low Mach number. Finally, the parallel efficiency of the scheme is evaluated on Canada’s largest supercomputer. It may be surprising to some that viscous flow behaviour can be accurately predicted by first-order PDEs. However, the applicability of hyperbolic moment methods to both continuum and non-equilibrium gas flows is now well established. Such a first-order treatment brings many physical and computational advantages to gas flow prediction.

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Lee, Jaejin. "Numerical Study of Three Dimensional Low Magnetic Reynolds Number Hypersonic Magnetohydrodynamic Flows." Scholarly Repository, 2011. http://scholarlyrepository.miami.edu/oa_dissertations/698.

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Hypersonic vehicles generate shocks that can heat the air sufficiently to partially ionize the air and create an electrically conducting plasma that can be studied using the equations of single fluid magnetohydrodynamics (MHD). Introducing strong applied magnetic and electric fields into the flow could have beneficial effects such as reducing heat damage, providing a sort of MHD parachute, and generating electric power or thrust in the vehicle. The Low Diffusion E-CUSP (LDE) scheme with a fifth order WENO scheme has recently been developed by Zha et al. [1, 2]. The purpose of this work is to incorporate the low magnetic Reynolds number MHD model and the thermodynamics of high temperature air to the above CFD algorithm so that it can be used to simulate hypersonic flows with MHD effects. In this work we compare results treating air as chemically frozen, neglecting all high temperature real gas effects with results obtained treating the air as a real gas in thermodynamic equilibrium, whose thermodynamic properties are changed by the high temperature. The hypersonic flows at high altitudes considered in this study have low Reynolds numbers. The Reynolds numbers range from about 2000 to 5000 for Mach 6 flows and reach up to 1200000 for Mach 15 flows. Thus, the flows are treated as laminar for the former cases and as turbulent for the latter using the Baldwin-Lomax turbulence model.

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Min, Ming. "Numerical Methods for European Option Pricing with BSDEs." Digital WPI, 2018. https://digitalcommons.wpi.edu/etd-theses/1169.

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This paper aims to calculate the all-inclusive European option price based on XVA model numerically. For European type options, the XVA can be calculated as so- lution of a BSDE with a specific driver function. We use the FT scheme to find a linear approximation of the nonlinear BSDE and then use linear regression Monte Carlo method to calculate the option price.

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Sabonis, Cynthia Anne. "Numerical Scheme for the Solution to Laplace's Equation using Local Conformal Mapping Techniques." Digital WPI, 2014. https://digitalcommons.wpi.edu/etd-theses/782.

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This paper introduces a method to determine the pressure in a fixed thickness, smooth, periodic domain; namely a lead-over-pleat cartridge filter. Finding the pressure within the domain requires the numerical solution of Laplace's equation, the first step of which is approximating, by interpolation, the curved portions of the filter to a circle in the xy plane.A conformal map is then applied to the filter, transforming the region into a rectangle in the uv plane. A finite difference method is introduced to numerically solve Laplace's equation in the rectangular domain. There are currently methods in existence to solve partial differential equations on non- regular domains. In a method employed by Monchmeyer and Muller, a scheme is used to transform from cartesian to spherical polar coordinates. Monchmeyer and Muller stress that for non-linear domains, extrapolation of existing cartesian difference schemes may produce incorrect solutions, and therefore, a volume centered discretization is used. A difference scheme is then derived that relies on mean values. This method has second order accuracy.(Rosenfeld,Moshe, Kwak, Dochan, 1989) The method introduced in this paper is based on a 7-point stencil which takes into account the unequal spacing of the points. From all neighboring pairs, a linear system of equations is constructed, which takes into account the periodic domain.This method is solved by standard iterative methods. The solution is then mapped back to the original domain, with second order accuracy. The method is then tested to obtain a solution to a domain which satisfies $y=sin(x)$ at the center, a shape similar to that of a lead-over-pleat cartridge filter. As a result, a model for the pressure distribution within the filter is obtained.

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Dansereau, Jeffrey Paul. "An analytic-numerical scheme for a collisional Fokker-Planck time dependent sheath-presheath structure." Thesis, Georgia Institute of Technology, 1987. http://hdl.handle.net/1853/17697.

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Zhang, Ziji. "Turbulent orifice flow in hydropower applications : a numerical and experimental study /." Doctoral thesis, Stockholm, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3209.

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Zhang, Shiyan. "Numerical Study of Sediment Transport under Unsteady Flow." Diss., The University of Arizona, 2011. http://hdl.handle.net/10150/202536.

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Numerical model for simulating sediment transport in unsteady flow is incomplete in several aspects: first of all, the numerical schemes have been proved suitable for the simulation of flow over rigid bed needs to be reevaluated for unsteady flow over mobile bed; secondly, existing non-equilibrium sediment transport models are empirically developed and therefore lack of consistency regarding the evaluation of the non-equilibrium parameters; thirdly, the sediment transport in various applications have unique features which needs to be considered in the models. Sediment transport in unsteady flows was studied using analytical and numerical methods. A one dimensional (1D) finite volume method (FVM) model was developed. Five popular numerical schemes were implemented into the model and their performances were evaluated under highly unsteady flow condition. A novel physically-based non-equilibrium sediment transport model was established to describe the non-equilibrium sediment transport process. Infiltration effects on flow and sediment transport was included to make the model applicable to simulate irrigation induced soil erosion in furrows. The Laursen (1958) formula was adopted and modified to calculate the erodibility of fine-grain sized soil, and then verified by laboratory and field datasets. The numerical model was applied to a series of simulations of sediment transport in highly unsteady flow including the dam break erosional flow, flash flood in natural rivers and irrigation flows and proved to be applicable in various applications. The first order schemes were able to produce smooth and reasonably accurate results, and spurious oscillations were observed in the simulated results produced by second order schemes. The proposed non-equilibrium sediment transport model yielded better results than several other models in the literatures. The modified Laursen (1958) formula adopted was applicable in calculating the erodibility of the soil in irrigation. Additionally, it was indicated that the effect of the jet erosion and the structural failure of the discontinuous bed topography cannot be properly accounted for due to the limitation of 1D model. The comparison between the simulated and measured sediment discharge hydrographs indicated a potential process associated to the transport of the fine-grain sized soil in the irrigation furrows.

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Bergersen, Bjørnar Dolva. "Numerical Solutions of Traffic Flow on Networks : Using the LWR-Model and the Godunov Scheme." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2014. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-25103.

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This paper shows how to create a simulationtool for traffic flow in a network using the Lighthill--Witham--Richards model and the Godunov scheme. First some basic rules about conservation laws are described and how to solve them using the method characteristics. This leads to the notion of weak solutions which can be solved by shock- and rarefractions-solutions. This is then used to describe how traffic behaves on a single road by using the LWR-model. The behavior of traffic at junctions is discussed, more specifically how to find the maximum flux through a junction when we deal with different amount of incoming and outgoing roads. The paper gives different examples of numerical solution methods to conservation laws, which gives motivation for the Godunov scheme. A numerical scheme using the LWR-model and the Godunov scheme is tested on different traffic models. The main test is a simplified model of Trondheim, Norway. The results are presented in videos, as well as graphs and tables that show the duration of the driving time through different routes of the model.

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Onay, Oguz Kaan. "Approximate Factorization Using Acdi Method On Hybrid Grids And Parallelization Of The Scheme." Master's thesis, METU, 2013. http://etd.lib.metu.edu.tr/upload/12615589/index.pdf.

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In this thesis study, a fast implicit iteration scheme called Alternating Cell Directions Imp licit method is combined with Approximate Factorization scheme. This application aims to offer a mathematically well defined version of the Alternating Cell Directions Implicit Method and increase the accuracy of the iteration scheme that is being used for the numerical solutions of the partial differential equations. The iteration scheme presented here is tested using unsteady diffusion equation, Laplace equation and advection-diffusion equation. The accuracy, convergence character and the stability character of the scheme compared with suitable iteration schemes for structured and unstructured quadrilateral grids. Besides, it is shown that the proposed scheme is applicable to triangular and hybrid polygonal grids. A transonic full potential solver is generated using the current scheme. The flow around a 2-D cylinder is solved for subcritical and supercritical cases. Axi-symmetric flow around cylinder is selected as a benchmark problem since the potential flow around bodies with a blunt leading edge is a more challenging problem than slender bodies. Besides, it is shown that, the method is naturally appropriate for parallelization using shared memory approach without using domain decomposition applications. The parallelization that is performed here is partially line, partially point parallelization. T he performance of the application is presented for a 3-D unsteady diffusion problem using Cartesian cells and 2-D unsteady diffusion problem using both structured and unstructured quadrilateral cells.

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22

Chaudru, de Raynal Paul Éric. "Équations différentielles stochastiques : résolubilité forte d'équations singulières dégénérées ; analyse numérique de systèmes progressifs-rétrogrades de McKean-Vlasov." Phd thesis, Université Nice Sophia Antipolis, 2013. http://tel.archives-ouvertes.fr/tel-00954417.

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Cette thèse traite de deux sujets: la résolubilité forte d'équations différentielles stochastiques à dérive hölderienne et bruit hypoelliptique et la simulation de processus progressifs-rétrogrades découplés de McKean-Vlasov. Dans le premier cas, on montre qu'un système hypoelliptique, composé d'une composante diffusive et d'une composante totalement dégénérée, est fortement résoluble lorsque l'exposant de la régularité Hölder de la dérive par rapport à la composante dégénérée est strictement supérieur à 2/3. Ce travail étend au cadre dégénéré les travaux antérieurs de Zvonkin (1974), Veretennikov (1980) et Krylov et Röckner (2005). L'apparition d'un seuil critique pour l'exposant peut-être vue comme le prix à payer pour la dégénérescence. La preuve repose sur des résultats de régularité de la solution de l'EDP associée, qui est dégénérée, et est basée sur une méthode parametrix. Dans le second cas, on propose un algorithme basé sur les méthodes de cubature pour la simulation de processus progessifs-rétrogrades découplés de McKean-Vlasov apparaissant dans des problèmes de contrôle dans un environnement de type champ moyen. Cet algorithme se divise en deux parties. Une première étape de construction d'un arbre de particules, à dynamique déterministe, approchant la loi de la composante progressive. Cet arbre peut être paramétré de manière à obtenir n'importe quel ordre d'approximation (en terme de pas de discrétisation de l'intervalle). Une seconde étape, conditionnelle à l'arbre, permettant l'approximation de la composante rétrograde. Deux schémas explicites sont proposés permettant un ordre d'approximation de 1 et 2.

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23

Vater, Stefan [Verfasser]. "A multigrid-based multiscale numerical scheme for shallow water flows at low froude number / Stefan Vater." Berlin : Freie Universität Berlin, 2013. http://d-nb.info/1033062561/34.

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24

Karra, Satish. "Modeling electrospinning process and a numerical scheme using Lattice Boltzmann method to simulate viscoelastic fluid flows." [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-1347.

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25

Bouwer, Abraham. "The Du Fort and Frankel finite difference scheme applied to and adapted for a class of finance problems." Diss., Pretoria : [s.n.], 2009. http://upetd.up.ac.za/thesis/available/etd-10122009-193152.

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26

Khan, Kamran-Ahmed. "A time integration scheme for stress - temperature dependent viscoelastic behaviors of isotropic materials." [College Station, Tex. : Texas A&M University, 2006. http://hdl.handle.net/1969.1/ETD-TAMU-1146.

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27

Tanaka, Daiki. "Stability Analysis of the CIP Scheme and its Applications in Fundamental Study of the Diffused Optical Tomography." 京都大学 (Kyoto University), 2014. http://hdl.handle.net/2433/188875.

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Bondarava, Alina Verfasser], and Klaus [Akademischer Betreuer] [Deckelnick. "Stability and error analysis for a numerical scheme to approximate elastic flow / Alina Bondarava. Betreuer: Klaus Deckelnick." Magdeburg : Universitätsbibliothek, 2015. http://d-nb.info/1082625825/34.

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29

Takamoto, Makoto. "A New Numerical Scheme For Resistive Relativistic Magnetohydrodynamics And Its Application to The Crab Pulsar Wind Nebula." 京都大学 (Kyoto University), 2012. http://hdl.handle.net/2433/157766.

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30

Bhutta, Bilal A. "A new parabolized Navier-Stokes scheme for hypersonic reentry flows." Diss., Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/52287.

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High Mach number, low-Reynolds number (high-altitude) reentry flowfield predictions are an important problem area in computational aerothermodynamics. Available numerical tools for handling such flows are very few and significantly limited in their applicability. A new implicit fully-iterative Parabolized Navier-Stokes (PNS) scheme is developed to accurately predict such low-Reynolds number flows. In this new approach the differential equations governing the conservation of mass, momentum and energy, and the algebraic equation of state for a perfect gas are solved simultaneously in a coupled manner. The idea is presented that by treating the governing equations in this manner (rather than eliminating the pressure terms in the governing equations by using appropriate differentiated forms of the equation of state) it may be possible to have an unconditionally time-like numerical scheme. The stability of a simplified version of this new PNS scheme is also studied, and it is demonstrated that these simplified equations are unconditionally time-like in the subsonic as well as the supersonic flow regions. A pseudo-time integration approach is used in addition to a new second-order accurate fully-implicit smoothing, to improve the efficiency of the solution algorithm. The new PNS scheme is used to predict the flowfield around a seven-deg sphere-cone vehicle under high- and low-Reynolds number conditions. Two test case, Case A and Case B, are chosen such that Case A has a large freestream Reynolds number (2.92x10⁵), whereas Case B has a freestream Reynolds number of 1.72x10³, which is smaller than the usual limit of applicability of the non-iterative PNS schemes (Re~10⁴ or larger). Comparisons are made with other available numerical schemes, and the results substantiate the stability, accuracy and efficiency claims of the new Parabolized Navier-Stokes scheme.
Ph. D.

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31

Ly, Eddie, and Eddie Ly@rmit edu au. "Numerical schemes for unsteady transonic flow calculation." RMIT University. Mathematics and Geospacial Sciences, 1999. http://adt.lib.rmit.edu.au/adt/public/adt-VIT20081212.163408.

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An obvious reason for studying unsteady flows is the prediction of the effect of unsteady aerodynamic forces on a flight vehicle, since these effects tend to increase the likelihood of aeroelastic instabilities. This is a major concern in aerodynamic design of aircraft that operate in transonic regime, where the flows are characterised by the presence of adjacent regions of subsonic and supersonic flow, usually accompanied by weak shocks. It has been a common expectation that the numerical approach as an alternative to wind tunnel experiments would become more economical as computers became less expensive and more powerful. However even with all the expected future advances in computer technology, the cost of a numerical flutter analysis (computational aeroelasticity) for a transonic flight remains prohibitively high. Hence it is vitally important to develop an efficient, cheaper (in the sense of computational cost) and physically accurate flutter simulation tech nique which is capable of reproducing the data, which would otherwise be obtained from wind tunnel tests, at least to some acceptable engineering accuracy, and that it is essentially appropriate for industrial applications. This need motivated the present research work on exploring and developing efficient and physically accurate computational techniques for steady, unsteady and time-linearised calculations of transonic flows over an aircraft wing with moving shocks. This dissertation is subdivided into eight chapters, seven appendices and a bibliography listing all the reference materials used in the research work. The research work initially starts with a literature survey in unsteady transonic flow theory and calculations, in which emphasis is placed upon the developments in these areas in the last three decades. Chapter 3 presents the small disturbance theory for potential flows in the subsonic, transonic and supersonic regimes, including the required boundary conditions and shock jump conditions. The flow is assumed irrotational and inviscid, so that the equation of state, continuity equation and Bernoulli's equation formulated in Appendices A and B can be employed to formulate the governing fluid equation in terms of total velocity potential. Furthermore for transonic flow with free-stream Mach number close to unity, we show in Appendix C that the shocks that appear are weak enough to allow us to neglect the flow rotationality. The formulations are based on the main assumption that aerofoil slopes are everywhere small, and the flow quantities are small perturbations about their free-stream values. In Chapter 4, we developed an improved approximate factorisation algorithm that solves the two-dimensional steady subsonic small disturbance equation with nonreflecting far-field boundary conditions. The finite difference formulation for the improved algorithm is presented in Appendix D, with the description of the solver used for solving the system of difference equations described in Appendix E. The calculation of steady and unsteady nonlinear transonic flows over a realistic aerofoil are considered in Chapter 5. Numerical solution methods, based on the finite difference approach, for solving the two-dimensional steady and unsteady, general-frequency transonic small disturbance equations are presented, with the corresponding finite difference formulation described in Appendix F. The theories and solution methods for the time-linearised calculations, in the frequency and time domains, for the problem of unsteady transonic flow over a thin planar wing undergoing harmonic oscillation are presented in Chapters 6 and 7, respectively. The time-linearised calculations include the periodic shock motion via the shock jump correction procedure. This procedure corrects the solution values behind the shock, to accommodate the effect of shock motion, and consequently, the solution method will produce a more accurate time-linearised solution for supercritical flow. Appendix G presents the finite difference formulation of these time-linearised solution methods. The aim is to develop an efficient computational method for calculating oscillatory transonic aerodynamic quantities efficiently for use in flutter analyses of both two- and three-dimensional wings with lifting surfaces. Chapter 8 closes the dissertation with concluding remarks and future prospects on the current research work.

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32

Sievers, Michael [Verfasser], Christian [Akademischer Betreuer] Meyer, and Dorothee [Gutachter] Knees. "A numerical scheme for rate-independent systems: analysis and realization / Michael Sievers ; Gutachter: Dorothee Knees ; Betreuer: Christian Meyer." Dortmund : Universitätsbibliothek Dortmund, 2020. http://d-nb.info/1225557038/34.

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33

Indratno, Sapto Wahyu. "Numerical methods for solving linear ill-posed problems." Diss., Kansas State University, 2011. http://hdl.handle.net/2097/8109.

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Doctor of Philosophy
Department of Mathematics
Alexander G. Ramm
A new method, the Dynamical Systems Method (DSM), justified recently, is applied to solving ill-conditioned linear algebraic system (ICLAS). The DSM gives a new approach to solving a wide class of ill-posed problems. In Chapter 1 a new iterative scheme for solving ICLAS is proposed. This iterative scheme is based on the DSM solution. An a posteriori stopping rules for the proposed method is justified. We also gives an a posteriori stopping rule for a modified iterative scheme developed in A.G.Ramm, JMAA,330 (2007),1338-1346, and proves convergence of the solution obtained by the iterative scheme. In Chapter 2 we give a convergence analysis of the following iterative scheme: u[subscript]n[superscript]delta=q u[subscript](n-1)[superscript]delta+(1-q)T[subscript](a[subscript]n)[superscript](-1) K[superscript]*f[subscript]delta, u[subscript]0[superscript]delta=0, where T:=K[superscript]* K, T[subscript]a :=T+aI, q in the interval (0,1),\quad a[subscript]n := alpha[subscript]0 q[superscript]n, alpha_0>0, with finite-dimensional approximations of T and K[superscript]* for solving stably Fredholm integral equations of the first kind with noisy data. In Chapter 3 a new method for inverting the Laplace transform from the real axis is formulated. This method is based on a quadrature formula. We assume that the unknown function f(t) is continuous with (known) compact support. An adaptive iterative method and an adaptive stopping rule, which yield the convergence of the approximate solution to f(t), are proposed in this chapter.

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34

Usman, Muhammad. "Performance Assessment and Management of Groundwater in an Irrigation Scheme by Coupling Remote Sensing Data and Numerical Modeling Approaches." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-203578.

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The irrigated agriculture in the Lower Chenab Canal (LCC) of Pakistan is characterized by huge water utilization both from surface and groundwater resources. Need of utilization of water from five rivers in Punjab province along with accelerated population growth has forced the construction of world’s largest irrigation network. Nevertheless, huge irrigation infrastructure, together with inappropriate drainage infrastructure, led to a build-up of shal-low groundwater levels, followed by waterlogging and secondary salinization in the soil profile. Following this era, decreased efficiency of irrigation supply system along with higher food demands had increased burdens on groundwater use, which led to a drop in groundwater levels in major parts of LCC. Previous studies in the study region revealed lacking management and maintenance of irrigation system, inflexible irrigation strategies, poor linkages between field level water supply and demands. No future strategy is present or under consideration to deal with this long time emerged groundwater situation particularly under unchanged irrigation water supply and climate change. Therefore, there is an utmost importance to assess the current profile of water use in the irrigation scheme and to device some workable strategies under future situations of land use and climate change. This study aims to investigate the spatio-temporal status of water utilization and performance of irrigation system using remote sensing data and techniques (SEBAL) in combination with other point data. Different irrigation performance indicators including equity, adequacy and reliability using evaporation fraction as main input parameter are utilized. Current profiles of land use/land cover (LULC) areas are assessed and their change detections are worked out to establish realistic future scenarios. Spatially distributed seasonal net recharge, a very important input parameter for groundwater modeling, is estimated by employing water balance approaches using spatial data from remote sensing and local norms. Such recharge results are also compared with a water table fluctuation approach. Following recharge estimation, a regional 3-D groundwater flow model using FEFLOW was set up. This model was calibrated by different approaches ranging from manual to automated pilot point (PP) approach. Sensitivity analysis was performed to see the model response against different model input parameters and to identify model regions which demand further improvements. Future climate parameters were downscaled to establish scenarios by using statistical downscaling under IPCC future emission scenarios. Modified recharge raster maps were prepared under both LULC and climate change scenarios and were fed to the groundwater model to investigate groundwater dynamics. Seasonal consumptive water use analysis revealed almost double use for kharif as compared to rabi cropping seasons with decrease from upper LCC to lower regions. Intra irrigation subdivision analysis of equity, an important irrigation performance indicator, shows less differences in water consumption in LCC. However, the other indicators (adequacy and reliability) indicate that the irrigation system is neither adequate nor reliable. Adequacy is found more pronounced during kharif as compared to rabi seasons with aver-age evaporation fraction of 0.60 and 0.67, respectively. Similarly, reliability is relatively higher in upper LCC regions as compared to lower regions. LULC classification shows that wheat and rice are major crops with least volatility in cultivation from season to season. The results of change detection show that cotton exhibited maximum positive change while kharif fodder showed maximum negative change during 2005-2012. Transformation of cotton area to rice cultivation is less conspicuous. The water consumption in upper LCC regions with similar crops is relatively higher as compared to lower regions. Groundwater recharge results revealed that, during the kharif cropping seasons, rainfall is the main source of recharge followed by field percolation losses, while for rabi cropping seasons, canal seepage remains the major source. Seasonal net groundwater recharge is mainly positive during all kharif seasons with a gradual increase in groundwater level in major parts of LCC. Model optimization indicates that PP is more flexible and robust as compared to manual and zone based approaches. Different statistical indicators show that this method yields reliable calibration and validation as values of Nash Sutcliffe Efficiency are 0.976 and 0.969, % BIAS are 0.026 and -0.205 and root mean square errors are 1.23 m and 1.31 m, respectively. Results of model output sensitivity suggest that hydraulic conductivity is a more influential parameter in the study area than drain/fillable porosity. Model simulation results under different scenarios show that rice cultivation has the highest impact on groundwater levels in upper LCC regions whereas major negative changes are observed for lower parts under decreased kharif fodder area in place of rice, cotton and sugarcane. Fluctuations in groundwater level among different proposed LULC scenarios are within ±1 m, thus showing a limited potential for groundwater management. For future climate scenarios, a rise in groundwater level is observed for 2011 to 2025 under H3A2 emission regime. Nevertheless, a drop in groundwater level is expected due to increased crop consumptive water use and decreased precipitations under H3A2 scenario for the periods 2026-2035 and 2036-2045. Although no imminent threat of groundwater shortage is anticipated, there is an opportunity for developing groundwater resources in the lower model regions through water re-allocation that would be helpful in dealing water shortages. The groundwater situation under H3B2 emission regime is relatively complex due to very low expectation of rise in groundwater level through precipitation during 2011-2025. Any positive change in groundwater under such scenarios is mainly associated with changes in crop consumptive water uses. Consequently, water management under such situation requires revisiting of current cropping patterns as well as augmenting water supply through additional surface water resources.

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35

Tanaka, Kenji. "Development of the new land surface scheme SiBUC commonly applicable to basin water management and numerical weather prediction model." 京都大学 (Kyoto University), 2005. http://hdl.handle.net/2433/145376.

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Kyoto University (京都大学)
0048
新制・論文博士
博士(工学)
乙第11576号
論工博第3817号
新制||工||1329(附属図書館)
22875
UT51-2004-U473
京都大学大学院工学研究科環境地球工学専攻
(主査)教授池淵周一, 教授椎葉充晴, 教授中北英一
学位規則第4条第2項該当

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36

Devantier, René, and Armin Raabe. "Mesoscale simulation of a heavy snowfall event over the Baltic Sea using an improved cloud parameterization scheme." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-212310.

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To model clouds in the mesoscale a 3D nonhydrostatic numerical model - GESIMA - was used, with a new cloud scheme which includes a quasispectral treatment of 6 different bulk water species ( water vapor, cloud water, rain, ice, snow, graupel) . lt allows to predict the distribution parameters since the number concentration and the mass mixing ratio were prognosed. So it is possible to vary the average particle masses ( diameters) in time which gives more realistic results. According to measurements two different distribution functions (log-normal for rain and cloud water and Marshall-Palmer for solid water classes) were used to describe the different water species. The cloud model is tested in a simulation of a mesoscale snowfall event over the southern Baltic Sea
Für die mesoskalige Simulation von Wolken wurde ein nichthydrostatisches numerisches 3D-Modell - GESIMA - benutzt, in dem ein neuer Wolkenmodul mit quasispektraler Behandlung 6 verschiedener Wolkenteilchenklassen (Wasserdampf, Wolkenwasser, Regen, Eis, Schnee, Graupel) implementiert wurde. Es erlaubt die Vorhersage der Verteilungsparameter, da sowohl die Teilchenzahlkonzentration als auch das Massenmischungsverhältnis prognostiziert werden. Damit ist es möglich auch die mittlere Masse (Durchmesser) einer Teilchensorte zeitlich zu variieren, was zu realistischeren Resultaten führt. In Übereinstimmung mit Messungen wurden 2 verschiedene Verteilungsfunktionen zur Beschreibung für die verschiedenen Teilchenklassen (log-normal für Wolkenwasser und Regen und Marshall-Palmer für Schnee und Graupel) benutzt. Das Wolkenmodell wurde in einer Simulation eines mesoskaligen Schneefallereignisses über der südwestlichen Ostsee getestet

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37

Kubrak, Boris. "Direct numerical simulation of gas transfer at the air-water interface in a buoyant-convective flow environment." Thesis, Brunel University, 2014. http://bura.brunel.ac.uk/handle/2438/10196.

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The gas transfer process across the air-water interface in a buoyant-convective environment has been investigated by Direct Numerical Simulation (DNS) to gain improved understanding of the mechanisms that control the process. The process is controlled by a combination of molecular diffusion and turbulent transport by natural convection. The convection when a water surface is cooled is combination of the Rayleigh-B´enard convection and the Rayleigh-Taylor instability. It is therefore necessary to accurately resolve the flow field as well as the molecular diffusion and the turbulent transport which contribute to the total flux. One of the challenges from a numerical point of view is to handle the very different levels of diffusion when solving the convection-diffusion equation. The temperature diffusion in water is relatively high whereas the molecular diffusion for most environmentally important gases is very low. This low molecular diffusion leads to steep gradients in the gas concentration, especially near the interface. Resolving the steep gradients is the limiting factor for an accurate resolution of the gas concentration field. Therefore a detailed study has been carried out to find the limits of an accurate resolution of the transport for a low diffusivity scalar. This problem of diffusive scalar transport was studied in numerous 1D, 2D and 3D numerical simulations. A fifth-order weighted non-oscillatory scheme (WENO) was deployed to solve the convection of the scalars, in this case gas concentration and temperature. The WENO-scheme was modified and tested in 1D scalar transport to work on non-uniform meshes. To solve the 2D and 3D velocity field the incompressible Navier-Stokes equations were solved on a staggered mesh. The convective terms were solved using a fourth-order accurate kinetic energy conserving discretization while the diffusive terms were solved using a fourth-order central method. The diffusive terms were discretized using a fourth-order central finite difference method for the second derivative. For the time-integration of the velocity field a second-order Adams-Bashworth method was employed. The Boussinesq approximation was employed to model the buoyancy due to temperature differences in the water. A linear relationship between temperature and density was assumed. A mesh sensitivity study found that the velocity field is fully resolved on a relatively coarse mesh as the level of turbulence is relatively low. However a finer mesh for the gas concentration field is required to fully capture the steep gradients that occur because of its low diffusivity. A combined dual meshing approach was used where the velocity field was solved on a coarser mesh and the scalar field (gas concentration and temperature) was solved on an overlaying finer submesh. The velocities were interpolated by a second-order method onto the finer sub-mesh. A mesh sensitivity study identified a minimum mesh size required for an accurate solution of the scalar field for a range of Schmidt numbers from Sc = 20 to Sc = 500. Initially the Rayleigh-B´enard convection leads to very fine plumes of cold liquid of high gas concentration that penetrate the deeper regions. High concentration areas remain in fine tubes that are fed from the surface. The temperature however diffuses much stronger and faster over time and the results show that temperature alone is not a good identifier for detailed high concentration areas when the gas transfer is investigated experimentally. For large timescales the temperature field becomes much more homogeneous whereas the concentration field stays more heterogeneous. However, the temperature can be used to estimate the overall transfer velocity KL. If the temperature behaves like a passive scalar a relation between Schmidt or Prandtl number and KL is evident. A qualitative comparison of the numerical results from this work to existing experiments was also carried out. Laser Induced Fluorescence (LIF) images of the oxygen concentration field and Schlieren photography has been compared to the results from the 3D simulations, which were found to be in good agreement. A detailed quantitative analysis of the process was carried out. A study of the horizontally averaged convective and diffusive mass flux enabled the calculation of transfer velocity KL at the interface. With KL known the renewal rate r for the so called surface renewal model could be determined. It was found that the renewal rates are higher than in experiments in a grid stirred tank. The horizontally averaged mean and fluctuating concentration profiles were analysed and from that the boundary layer thickness could be accurately monitored over time. A lot of this new DNS data obtained in this research might be inaccessible in experiments and reveal previously unknown details of the gas transfer at the air water interface.

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Chandra, Santanu. "A NUMERICAL STUDY FOR LIQUID BRIDGE BASED MICROGRIPPING AND CONTACT ANGLE MANIPULATION BY ELECTROWETTING METHOD." University of Akron / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=akron1197299987.

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39

Cozma, Andrei. "Numerical methods for foreign exchange option pricing under hybrid stochastic and local volatility models." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:44a27fbc-1b7a-4f1a-bd2d-abeb38bf1ff7.

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In this thesis, we study the FX option pricing problem and put forward a 4-factor hybrid stochastic-local volatility model. The model, which describes the dynamics of an exchange rate, its volatility and the domestic and foreign short rates, allows for a perfect calibration to European options and has a good hedging performance. Due to the high-dimensionality of the problem, we propose a Monte Carlo simulation scheme that combines the full truncation Euler scheme for the stochastic volatility component and the stochastic short rates with the log-Euler scheme for the exchange rate. We analyze exponential integrability properties of Euler discretizations for the square-root process driving the stochastic volatility and the short rates, properties which play a key role in establishing the finiteness of moments and the strong convergence of numerical approximations for a large class of stochastic differential equations in finance, including the ones studied in this thesis. Hence, we prove the strong convergence of the exchange rate approximations and the convergence of Monte Carlo estimators for a number of vanilla and exotic options. Then, we calibrate the model to market data and discuss its fitness for pricing FX options. Next, due to the relatively slow convergence of the Monte Carlo method in the number of simulations, we examine a variance reduction technique obtained by mixing Monte Carlo and finite difference methods via conditioning. We consider a purely stochastic version of the model and price vanilla and exotic options by simulating the paths of the volatility and the short rates, and then evaluating the "inner" Black-Scholes-type expectation by means of a partial differential equation. We prove the convergence of numerical approximations and carry out a theoretical variance reduction analysis. Finally, we illustrate the efficiency of the method through a detailed quantitative assessment.

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40

Kunadian, Illayathambi. "NUMERICAL INVESTIGATION OF THERMAL TRANSPORT MECHANISMS DURING ULTRA-FAST LASER HEATING OF NANO-FILMS USING 3-D DUAL PHASE LAG (DPL) MODEL." UKnowledge, 2004. http://uknowledge.uky.edu/gradschool_theses/324.

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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.

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41

Devantier, René, and Armin Raabe. "Mesoscale simulation of a heavy snowfall event over the Baltic Sea using an improved cloud parameterization scheme." Universität Leipzig, 1995. https://ul.qucosa.de/id/qucosa%3A15015.

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To model clouds in the mesoscale a 3D nonhydrostatic numerical model - GESIMA - was used, with a new cloud scheme which includes a quasispectral treatment of 6 different bulk water species ( water vapor, cloud water, rain, ice, snow, graupel) . lt allows to predict the distribution parameters since the number concentration and the mass mixing ratio were prognosed. So it is possible to vary the average particle masses ( diameters) in time which gives more realistic results. According to measurements two different distribution functions (log-normal for rain and cloud water and Marshall-Palmer for solid water classes) were used to describe the different water species. The cloud model is tested in a simulation of a mesoscale snowfall event over the southern Baltic Sea.
Für die mesoskalige Simulation von Wolken wurde ein nichthydrostatisches numerisches 3D-Modell - GESIMA - benutzt, in dem ein neuer Wolkenmodul mit quasispektraler Behandlung 6 verschiedener Wolkenteilchenklassen (Wasserdampf, Wolkenwasser, Regen, Eis, Schnee, Graupel) implementiert wurde. Es erlaubt die Vorhersage der Verteilungsparameter, da sowohl die Teilchenzahlkonzentration als auch das Massenmischungsverhältnis prognostiziert werden. Damit ist es möglich auch die mittlere Masse (Durchmesser) einer Teilchensorte zeitlich zu variieren, was zu realistischeren Resultaten führt. In Übereinstimmung mit Messungen wurden 2 verschiedene Verteilungsfunktionen zur Beschreibung für die verschiedenen Teilchenklassen (log-normal für Wolkenwasser und Regen und Marshall-Palmer für Schnee und Graupel) benutzt. Das Wolkenmodell wurde in einer Simulation eines mesoskaligen Schneefallereignisses über der südwestlichen Ostsee getestet.

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42

Multani, Sahib Singh. "Pseudospectral Collocation Method Based Energy Management Scheme for a Parallel P2 Hybrid Electric Vehicle." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1587653689067271.

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Munkejord, Svend Tollak. "Analysis of the two-fluid model and the drift-flux model for numerical calculation of two-phase flow." Doctoral thesis, Norwegian University of Science and Technology, Faculty of Engineering Science and Technology, 2006. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-679.

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Flerfasestrømning er av betydning i en lang rekke anvendelser, blant annet i olje- og gassindustrien, i den kjemiske og i prosessindustrien, inkludert i varmepumpende systemer, samt i sikkerhetsanalyse av kjernekraftverk. Denne avhandlingen analyserer modeller for tofasestrømning, og metoder for numerisk løsning av disse modellene. Den er derfor ett bidrag til å utvikle pålitelige ingeniørverktøy for flerfase-anvendelser. Slike verktøy trengs og forventes av ingeniører i industrien.

Den tilnærmede Riemann-løseren framsatt av Roe har blitt studert. Roe-skjema for tre ulike modeller for tofasestrømning har blitt implementert i rammen av en standard numerisk algoritme for løsning av hyperbolske bevaringslover. Disse skjemaene har blitt analysert ved hjelp av referanse-regnestykker fra litteraturen, og ved sammenlikning med hverandre.

Et Roe-skjema for den fire-liknings ettrykks tofluid-modellen har blitt implementert, og det har blitt vist at en andreordens utvidelse basert på bølge-dekomponering og fluksdifferanse-splitting virker godt, og gir forbedrede resultater sammenliknet med det førsteordens skjemaet.

Det har blitt foreslått et Roe-skjema for en fem-liknings totrykks tofluid-modell med trykkrelaksering. Bruken av analoge numeriske metoder for fire-liknings- og fem-liknings-modellene gjorde det mulig med en direkte sammenlikning av en metode med og uten trykkrelaksering. Numeriske eksperiment demonstrerte at de to framgangsmåtene konvergerte til samme resultat, men at den fem-liknings trykkrelakserings-metoden var betydelig mer dissipativ, særlig for kontakt-diskontinuiteter. Videre viste beregninger at selv om fem-liknings-modellen har reelle egenverdier, så produserte den oscillasjoner for tilfeller der fire-liknings-modellen hadde komplekse egenverdier.

Et Roe-skjema har blitt konstruert for driftfluks-modellen med generelle lukningslover. Roe-matrisen er helt analytisk for det tilfellet at man kan anvende Zuber-Findlay-slipp-loven som beskriver boblestrømning. Dermed er dette Roe-skjemaet mer effektivt enn tidligere fullt numeriske Roe-skjema for driftfluks-modellen.

En isentropisk diskret-nivå-flerfasemodell har blitt presentert. En diskusjon av hvordan man kan ta hensyn til ulike interfase-trykkmodeller har blitt gitt. Med de passende modellene for interfase-trykk og -fart, var samsvaret svært godt mellom diskret-nivå-modellen og det fem-liknings Roe-skjemaet.

Multi-steg- (MUSTA) metoden har som siktemål å komme nær oppstrøms-metodene i nøyaktighet, samtidig som den bevarer enkelheten til sentrerte skjema. Her har metoden blitt brukt på driftfluks-modellen. Når antallet steg økes, nærmer resultatene fra MUSTA-metoden seg det man får med Roe-metoden. De gode resultatene til MUSTA-metoden er avhengige av at man bruker et stort nok lokalt grid. Derfor er hovedfordelen med MUSTA-metoden at den er enkel, snarere enn at man sparer regnetid.

En karakteristikk-basert metode for å spesifisere grensebetinglser for flerfase-modeller har blitt testet, og funnet å virke godt for transiente problem.

This thesis analyses models for two-phase flows and methods for the numerical resolution of these models. It is therefore one contribution to the development of reliable design tools for multiphase applications. Such tools are needed and expected by engineers in a range of fields, including in the oil and gas industry.

The approximate Riemann solver of Roe has been studied. Roe schemes for three different two-phase flow models have been implemented in the framework of a standard numerical algorithm for the solution of hyperbolic conservation laws. The schemes have been analysed by calculation of benchmark tests from the literature, and by comparison with each other.

A Roe scheme for the four-equation one-pressure two-fluid model has been implemented, and a second-order extension based on wave decomposition and flux-difference splitting was shown to work well and to give improved results compared to the first-order scheme. The convergence properties of the scheme were tested on smooth and discontinuous solutions.

A Roe scheme has been proposed for a five-equation two-pressure two-fluid model with pressure relaxation. The use of analogous numerical methods for the five-equation and four-equation models allowed for a direct comparison of a method with and without pressure relaxation. Numerical experiments demonstrated that the two approaches converged to the same results, but that the five-equation pressure-relaxation method was significantly more dissipative, particularly for contact discontinuities. Furthermore, even though the five-equation model with instantaneous pressure relaxation has real eigenvalues, the calculations showed that it produced oscillations for cases where the four-equation model had complex eigenvalues.

A Roe scheme has been constructed for the drift-flux model with general closure laws. For the case of the Zuber-Findlay slip law describing bubbly flows, the Roe matrix is completely analytical. Hence the present Roe scheme is more efficient than previous fully numerical Roe schemes for the drift-flux model.

An isentropic discrete-equation multiphase model has been presented. The incorporation of different interfacial-pressure models was discussed, and examples were given. With the adequate models for the interfacial pressure and velocity, the agreement was very good between the discrete-equation model and the five-equation Roe scheme.

The flux-limiter centred (FLIC) scheme was tested for the four-equation two-fluid model. Only the first-order version (FORCE) of the scheme was found to work well, but it was rather diffusive. The purpose of the multi-stage (MUSTA) method is to come close to the accuracy of upwind schemes while retaining the simplicity of centred schemes. Here it has been applied to the drift-flux model. As the number of stages was increased, the results of the MUSTA scheme approached those of the Roe method. The good results of the MUSTA scheme were dependent on the use of a large-enough local grid. Hence, the main advantage of the MUSTA scheme is its simplicity.

A multiphase characteristic-based boundary-condition method has been tested, and it was shown to be workable for transient problems.

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Wang, Zhengquan. "A Hybrid Pseudodynamic Testing Platform for Structural Engineering Research – Application for the Development of an Innovative Retrofit Scheme." Cincinnati, Ohio University of Cincinnati, 2007. http://www.ohiolink.edu/etd/view.cgi?ucin1178625931.

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Thesis (Ph.D.)--University of Cincinnati, 2007.
Title from electronic thesis title page (viewed July 10, 2007). Includes abstract. Keywords: Pseudodynamic Testing; Pre-testing Simulation; Implicit Numerical Method; Special Braced Buildings; Buckling-Enhanced Braces Includes bibliographical references.

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Ricchiuto, Mario. "Contributions to the development of residual discretizations for hyperbolic conservation laws with application to shallow water flows." Habilitation à diriger des recherches, Université Sciences et Technologies - Bordeaux I, 2011. http://tel.archives-ouvertes.fr/tel-00651688.

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In this work we review 12 years of developments in the field of residual based discretizations for hyperbolic problems and their application to the solution of the shallow water equations. Fundamental concepts related to the topic are recalled and he construction of second and higher order schemes for steady problems is presented. The generalization to time dependent problems by means of multi-step implicit time integration, space-time, and genuinely explicit techniques is thoroughly discussed. Finally, the issues of C-property, super consistency, and wetting/drying are analyzed in this framework showing the power of the residual based approach.

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Wu, Jian. "Contribution to numerical simulation of electrohydrodynamics flows : application to electro-convection and electro-thermo-convection between two parallel plates." Thesis, Poitiers, 2012. http://www.theses.fr/2012POIT2263/document.

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Dans cette thèse, nous présentons une nouvelle approche pour la simulation numérique des phénomènes électroconvectifs et électro-therrno-convectifs. La principale difficulté réside dans la détermination du champ électrique et de la distribution de densité volurnique de charges électriques. Dans cette approche, des schémas de type TVD (Total Variation Dirninishing) et IDC (ImprovedDeferred Correction) sont utilisées dans la discrétisation des flux convectifs et diffusifs par la méthode des volumes finis. La première partie de cette thèse présente certains aspects numériques liés à l'implémentation de ces schémas. Une approche unifiée pour les schémas convectifs TVD de type borné à haute résolution est présentée et diverses fonctions limiteur sont comparées. Dans une deuxième partie, l'électro-convection entre deux plaques parallèles est simulée. La méthodologie a étéévaluée et validée par la détermination des Critères de stabilité linéaire et non linéaire. Les différents scenarii d'évolution du développement de cette instabilité électroconvective vers l'état chaotique ont été définis. L'effet du mécanisme de diffusion la densité volumique de charge sur la boucle d'hystérésis et sur la structure de l'écoulement est étudié. L'influence du rapport d'aspect de la cavité est analysé. Enfin dans une dernière partie, nous étudions l'électro-thermo-convection lorsque le fluide est soumis simultanément à une injection unipolaire et à un gradient thermique. L'augmentation des transferts de chaleur a été caractérisée
In this thesis, a numerical approach is presented to simulate the electro- and electro-thermo convection in dielectric liquids. The total variation diminishing (TVD) scheme and improved deferred correction (IDC) scheme are used to compute the convective and diffusive respectively. The aim of TVD scheme is to avoid non-physical oscillations and to capture high gradient of charge density. Some fundarnental aspects related to TVD and LDC schemes are investigated firstly. A unified approach for TVD schemes is explained and various limiter functions are compared. The connection among three methods for diffusive flux computation has been revealed. The original IDC scheme is improved by the application of 2nd order gradient evaluation method.The electro-convection between two parallel plates is then simulated. The methodology was assessed by the determination of the linear and nonlinear stability criterion. By continuously increasing the driving parameter, the successive instabilities and route to chaotic state has been defined. The effects of the diffusion mechanism for the charge density and vertical walls on the hysteresis 100p and the structure are also investigated. The last part is to simuiate electro-thermo-convection when injection and thermal gradient are simultaneously applied. Our solver was verified with a stationary and an overstable stability problem.The case that both heating and injection are from a bottom electrode has been analyzed in details. The neutral stabiliïy curve was reproduced. The existence of nonlinear phenornenon and the structure are highlighted

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Tschisgale, Silvio. "A numerical method for fluid-structure interactions of slender rods in turbulent flow." TUDpress - Thelem Universitätsverlag, 2018. https://tud.qucosa.de/id/qucosa%3A38706.

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This thesis presents a numerical method for the simulation of fluid-structure interaction (FSI) problems on high-performance computers. The proposed method is specifically tailored to interactions between Newtonian fluids and a large number of slender viscoelastic structures, the latter being modeled as Cosserat rods. From a numerical point of view, such kind of FSI requires special techniques to reach numerical stability. When using a partitioned fluid-structure coupling approach this is usually achieved by an iterative procedure, which drastically increases the computational effort. In the present work, an alternative coupling approach is developed based on an immersed boundary method (IBM). It is unconditionally stable and exempt from any global iteration between the fluid part and the structure part. The proposed FSI solver is employed to simulate the flow over a dense layer of vegetation elements, usually designated as canopy flow. The abstracted canopy model used in the simulation consists of 800 strip-shaped blades, which is the largest canopy-resolving simulation of this type done so far. To gain a deeper understanding of the physics of aquatic canopy flows the simulation data obtained are analyzed, e.g., concerning the existence and shape of coherent structures.

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Coussement, Axel. "Direct numerical simulation and reduced chemical schemes for combustion of perfect and real gases." Doctoral thesis, Universite Libre de Bruxelles, 2012. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209765.

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La première partie de cette thèse traite du développement du code de simulation numérique directe YWC, principalement du développement des conditions aux limites. En effet, une forte contribution scientifique a été apportée aux conditions aux limites appelées "Three dimensional Navier-Stokes characteristic boundary condtions" (3D-NSCBC). Premièrement, la formulation de ces conditions aux arêtes et coins a été complétée, ensuite une extension de la formulation a été proposée pour supprimer les déformations observées en sortie dans le cas d'écoulements non-perpendiculaires à la frontière.

De plus, ces conditions ont été étendues au cas des gaz réels et une nouvelle définition du facteur de relaxation pour la pression a été proposée. Ce nouveau facteur de relaxation permet de supprimer les déformations observées en sortie pour des écoulements transcritiques.

Les résultats obtenus avec le code YWC ont ensuite été utilisés dans la seconde partie de la thèse pour développer une nouvelle méthode de tabulation basée sur l'analyse en composantes principales. Par rapport aux méthodes existante telles que FPI ou SLFM, la technique proposée, permet une identification automatique des variables à transporter et n'est, de plus, pas lié à un régime de combustion spécifique. Cette technique a permis d'effectuer des calculs d'interaction flamme-vortex en ne transportant que 5 espèces à la place des 9 requises pour le calcul en chimie détaillée complète, sans pour autant perdre en précision.

Finalement, dans le but de réduire encore le nombre d'espèces transportées, les techniques T-BAKED et HT-BAKED PCA ont été introduites. En utilisant une pondération des points sous-représentés, ces deux techniques permettent d'augmenter la précision de l'analyse par composantes principales dans le cadre des phénomènes de combustion.

Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished

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Sladkov, Andrey. "Numerical modeling of magnetic reconnection in laser-induced high energy density plasmas." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS376.

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Cette thèse est une étude numérique de la reconnexion magnétique dans les plasmas sans collision à l’aide d’un code cinétique. On peut étudier le processus de reconnexion magnétique lors d'expérience pour lesquels le plasma est créé par interaction d’un laser de puissance sur une cible solide. Durant cette thèse, nous avons inclus dans le code HECKLE les éléments permettant de rendre ces simulations plus réalistes pour les conditions lasers: les effets du tenseur complet des électrons ainsi que l’expansion super-Alfvénique du plasma. Nous avons ainsi mis en évidence le rôle du tenseur de pression pour réduire l’efficacité de la reconnexion, ainsi que les effets de température du plasma la rendant plus impulsionnelle
This thesis is a numerical study of the magnetic reconnection in collisionless plasmas using a kinetic code. We can study the magnetic reconnection process during experiments for which the plasma is created by interaction of a power laser on a solid target. During this thesis, we included in the HECKLE code the elements allowing to make these simulations more realistic for the laser conditions: the effects of the electron six-component pressure tensor as well as the super-Alfvénic expansion of the plasma. We have thus highlighted the role of the pressure tensor to reduce the efficiency of the reconnection, as well as the plasma temperature effects making it more impulsive

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Viot, Louis. "Couplage et synchronisation de modèles dans un code scénario d’accidents graves dans les réacteurs nucléaires." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLN033/document.

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La thèse s'inscrit dans le contexte des accidents graves dans les réacteurs nucléaires qui sont étudiés au laboratoire de physique et modélisation des accidents graves (LPMA) du CEA de Cadarache. Un accident grave survient lors de la perte du caloporteur au niveau du circuit primaire ce qui provoque une dégradation du combustible et la création d'un bain de corium. Celui-ci va ensuite se propager en cuve et fortement endommager les structures du réacteur. Pour la sûreté nucléaire, il est donc nécessaire de pouvoir prévoir la propagation de ce corium, d'où la création en 2013 de la plateforme PROCOR (Java) permettant aux travers d'applications industrielles de simuler cette propagation. Ces applications sont un ensemble de modèles physiques, couplés sur une macro boucle en temps, ayant chacun un ensemble d'équations algébriques et différentielles qui sont résolues en interne des modèles. Les modèles de la plateforme sont généralement des modèles OD dont la discrétisation spatiale est remplacée par des corrélations généralement issues de l'expérience. Chaque modèle a aussi un ensemble d'états et de règles de transition, et un changement d'état peut alors survenir à l'intérieur de la macro boucle en temps. Au début de la thèse, le couplage était simplement un chaînage des modèles sur la macro boucle en temps : chaque modèle est résolu l'un après l'autre, l'ordre étant défini par le créateur de l'application, et les modèles sont synchronisés à la fin de cette boucle. Les résultats des applications industrielles de la plateforme en modifiant simplement le pas de temps de la macro boucle en temps montrent une forte dépendance du schéma avec ce pas de temps. On a par exemple 10 % d'écart sur les flux imposés sur la cuve du réacteur en passant d'un pas de temps de 100 s à 50 s, ce qui a un fort impact sur les résultats de sûreté nucléaire
This thesis focuses on solving coupled problems of models of interest for the simulation of severe accidents in nuclear reactors~: these coarse-grained models allow for fast calculations for statistical analysis used for risk assessment and solutions of large problems when considering the whole severe accident scenario. However, this modeling approach has several numerical flaws. Besides, in this industrial context, computational efficiency is of great importance leading to various numerical constraints. The objective of this research is to analyze the applicability of explicit coupling strategies to solve such coupled problems and to design implicit coupling schemes allowing stable and accurate computations. The proposed schemes are theoretically analyzed and tested within CEA's procor{} platform on a problem of heat conduction solved with coupled lumped parameter models and coupled 1D models. Numerical results are discussed and allow us to emphasize the benefits of using the designed coupling schemes instead of the usual explicit coupling schemes

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