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1
Aregba-Driollet, D., R. Natalini, and S. Tang. "Explicit diffusive kinetic schemes for nonlinear degenerate parabolic systems." Mathematics of Computation 73, no. 245 (August 26, 2003): 63–94. http://dx.doi.org/10.1090/s0025-5718-03-01549-7.
2
Dimarco, Giacomo, Lorenzo Pareschi, and Vittorio Rispoli. "Implicit-Explicit Runge-Kutta Schemes for the Boltzmann-Poisson System for Semiconductors." Communications in Computational Physics 15, no. 5 (May 2014): 1291–319. http://dx.doi.org/10.4208/cicp.090513.151113a.
Анотація:
AbstractIn this paper we develop a class of Implicit-Explicit Runge-Kutta schemes for solving the multi-scale semiconductor Boltzmann equation. The relevant scale which characterizes this kind of problems is the diffusive scaling. This means that, in the limit of zero mean free path, the system is governed by a drift-diffusion equation. Our aim is to develop a method which accurately works for the different regimes encountered in general semiconductor simulations: the kinetic, the intermediate and the diffusive one. Moreover, we want to overcome the restrictive time step conditions of standard time integration techniques when applied to the solution of this kind of phenomena without any deterioration in the accuracy. As a result, we obtain high order time and space discretization schemes which do not suffer from the usual parabolic stiffness in the diffusive limit. We show different numerical results which permit to appreciate the performances of the proposed schemes.
3
Boudin, Laurent, Céline Grandmont, Bérénice Grec, Sébastien Martin, Amina Mecherbet, and Frédérique Noël. "Fluid-kinetic modelling for respiratory aerosols with variable size and temperature." ESAIM: Proceedings and Surveys 67 (2020): 100–119. http://dx.doi.org/10.1051/proc/202067007.
Анотація:
In this paper, we propose a coupled fluid-kinetic model taking into account the radius growth of aerosol particles due to humidity in the respiratory system. We aim to numerically investigate the impact of hygroscopic effects on the particle behaviour. The air flow is described by the incompressible Navier-Stokes equations, and the aerosol by a Vlasov-type equation involving the air humidity and temperature, both quantities satisfying a convection-diffusion equation with a source term. Conservations properties are checked and an explicit time-marching scheme is proposed. Twodimensional numerical simulations in a branched structure show the influence of the particle size variations on the aerosol dynamics.
4
Huh, Joo Youl, and Jong Pa Hong. "Influences of Elastic Stress and Interfacial Kinetic Barrier on Phase Evolution Paths of Thin-Film Diffusion Couples." Solid State Phenomena 118 (December 2006): 405–12. http://dx.doi.org/10.4028/www.scientific.net/ssp.118.405.
Анотація:
An explicit, finite difference scheme was used to examine the effects of coherency stresses and interface kinetic barriers on the phase evolution of a binary, thin-film diffusion couple. Thin-films, initially consisting of alternating layers of two terminal phases, α and γ, were held at a temperature at which the formation of an intermediate phase, β, at α/γ interface was thermodynamically probable. When either the coherency stresses or interface kinetic barriers are present, the interfacial compositions become time-dependent and, thus, the formation of the thermodynamically stable β phase can be kinetically prohibited at the early stage of the evolution. Even if the initial α/γ thin-films have the same overall composition, the coherency constraint can result in different final equilibrium states depending on either the initial compositions of the α and γ phases or the relative magnitudes of the interfacial kinetic barriers. When both the coherency constraint and interfacial kinetic barriers are present, an intermediate phase can repeatedly form and disappear during the evolution.
5
Eckermann, Stephen D. "Explicitly Stochastic Parameterization of Nonorographic Gravity Wave Drag." Journal of the Atmospheric Sciences 68, no. 8 (August 1, 2011): 1749–65. http://dx.doi.org/10.1175/2011jas3684.1.
Анотація:
Abstract A straightforward methodology is presented for converting the deterministic multiwave parameterizations of nonorographic gravity wave drag, currently used in general circulation models (GCMs), to stochastic analogs that use fewer waves (in the example herein, a single wave) within each grid box. Deterministic discretizations of source-level momentum flux spectra using a fixed spectrum of many waves with predefined phase speeds are replaced by sampling these source spectra stochastically using waves with randomly assigned phase speeds. Using simple conversion formulas, it is shown that time-mean wave-induced drag, diffusion, and heating-rate profiles identical to those from the deterministic scheme are produced by the stochastic analog. Furthermore, in these examples the need for bulk intermittency factors of small value is largely obviated through the explicit incorporation of stochastic intermittency into the scheme. When implemented in a GCM, the single-wave stochastic analog of an existing deterministic scheme reproduces almost identical time-mean middle-atmosphere climate and drag as its deterministic antecedent but with an order of magnitude reduction in computational expense. The stochastically parameterized drag is also accompanied by inherent variability about the time-mean profile that forces the smallest space–time scales of the GCM. Studies of mean GCM kinetic energy spectra show that this additional stochastic forcing does not lead to excessive increases in dynamical variability at these smallest GCM scales. The results show that the expensive deterministic schemes currently used in GCMs are easily modified and replaced by cheap stochastic analogs without any obvious deleterious impacts on GCM climate or variability, while offering potential advantages of computational savings, reduction of systematic climate biases, and greater and more realistic ensemble spread.
6
Chepak-Gizbrekht, M. V., and A. G. Knyazeva. "Two-dimensional model of grain boundary diffusion and oxidation." PNRPU Mechanics Bulletin, no. 1 (December 15, 2022): 156–66. http://dx.doi.org/10.15593/perm.mech/2022.1.12.
Анотація:
The grinding of the structure of materials is accompanied by a change in the physical and mechanical properties. This occurs largely due to the accumulation of energy and defects in the structure, which activates the diffusion of impurities contained in the material. The increase in the number of grain boundaries and joints can cause the inelastic behavior of the material, its additional chemical activation. For some metals and alloys this leads to strengthening, while for others it leads to rapid degradation of mechanical properties. Grain boundary diffusion in such materials is the main mechanism of transport of alloying components or harmful impurities, so its study is important. This paper presents a two-dimensional model of grain boundary diffusion in a material with an explicit structure assignment. The model takes into account the presence of chemical transformations that can determine the corrosion mechanisms under operating conditions. For simplicity of calculation the material structure is taken symmetrical and contains two phases: grains and a boundary phase. Diffusion and kinetic parameters of the phases may differ. The model is represented in dimensionless form so that the distances between neighboring grains or the widths of the boundary phase are the same and the grain sizes can vary. Depending on the ratio of phase sizes we can speak about micro- and nanocrystalline structure. The problem was solved numerically using implicit difference scheme and coordinate splitting. Diffusion and kinetic parameters, which are close to the parameters of oxygen grain boundary diffusion in titanium and titanium oxidation, respectively, were taken for the calculations. Integral concentrations reflect the dynamics (kinetics) of oxygen and oxides accumulation over the calculation area. Results showing the role of changes in the oxidation kinetics due to changes in the reaction constants in the phases and the phase size ratio are presented. The model can be useful for assessing the degree of influence of grain boundary diffusion on the oxidation process and the accompanying change in properties, as well as for setting up appropriate experiments.
7
Muñoz-Esparza, Domingo, Robert D. Sharman, and Stanley B. Trier. "On the Consequences of PBL Scheme Diffusion on UTLS Wave and Turbulence Representation in High-Resolution NWP Models." Monthly Weather Review 148, no. 10 (October 1, 2020): 4247–65. http://dx.doi.org/10.1175/mwr-d-20-0102.1.
Анотація:
AbstractMesoscale numerical weather prediction (NWP) models are routinely exercised at kilometer-scale horizontal grid spacings (Δx). Such fine grids will usually allow at least partial resolution of small-scale gravity waves and turbulence in the upper troposphere and lower stratosphere (UTLS). However, planetary boundary layer (PBL) parameterization schemes used with these NWP model simulations typically apply explicit subgrid-scale vertical diffusion throughout the entire vertical extent of the domain, an effect that cannot be ignored. By way of an example case of observed widespread turbulence over the U.S. Great Plains, we demonstrate that the PBL scheme’s mixing in NWP model simulations of Δx = 1 km can have significant effects on the onset and characteristics of the modeled UTLS gravity waves. Qualitatively, PBL scheme diffusion is found to affect not only background conditions responsible for UTLS wave activity, but also to control the local vertical mixing that triggers or hinders the onset and propagation of these waves. Comparisons are made to a reference large-eddy simulation with Δx = 250 m to statistically quantify these effects. A significant and systematic overestimation of resolved vertical velocities, wave-scale fluxes, and kinetic energy is uncovered in the 1-km simulations, both in clear-air and in-cloud conditions. These findings are especially relevant for upper-level gravity wave and turbulence simulations using high-resolution kilometer-scale NWP models.
8
Deng, Aijun, and David R. Stauffer. "On Improving 4-km Mesoscale Model Simulations." Journal of Applied Meteorology and Climatology 45, no. 3 (March 1, 2006): 361–81. http://dx.doi.org/10.1175/jam2341.1.
Анотація:
Abstract A previous study showed that use of analysis-nudging four-dimensional data assimilation (FDDA) and improved physics in the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5) produced the best overall performance on a 12-km-domain simulation, based on the 18–19 September 1983 Cross-Appalachian Tracer Experiment (CAPTEX) case. However, reducing the simulated grid length to 4 km had detrimental effects. The primary cause was likely the explicit representation of convection accompanying a cold-frontal system. Because no convective parameterization scheme (CPS) was used, the convective updrafts were forced on coarser-than-realistic scales, and the rainfall and the atmospheric response to the convection were too strong. The evaporative cooling and downdrafts were too vigorous, causing widespread disruption of the low-level winds and spurious advection of the simulated tracer. In this study, a series of experiments was designed to address this general problem involving 4-km model precipitation and gridpoint storms and associated model sensitivities to the use of FDDA, planetary boundary layer (PBL) turbulence physics, grid-explicit microphysics, a CPS, and enhanced horizontal diffusion. Some of the conclusions include the following: 1) Enhanced parameterized vertical mixing in the turbulent kinetic energy (TKE) turbulence scheme has shown marked improvements in the simulated fields. 2) Use of a CPS on the 4-km grid improved the precipitation and low-level wind results. 3) Use of the Hong and Pan Medium-Range Forecast PBL scheme showed larger model errors within the PBL and a clear tendency to predict much deeper PBL heights than the TKE scheme. 4) Combining observation-nudging FDDA with a CPS produced the best overall simulations. 5) Finer horizontal resolution does not always produce better simulations, especially in convectively unstable environments, and a new CPS suitable for 4-km resolution is needed. 6) Although use of current CPSs may violate their underlying assumptions related to the size of the convective element relative to the grid size, the gridpoint storm problem was greatly reduced by applying a CPS to the 4-km grid.
9
YOSSIFON, G., I. FRANKEL, and T. MILOH. "Macro-scale description of transient electro-kinetic phenomena over polarizable dielectric solids." Journal of Fluid Mechanics 620 (February 10, 2009): 241–62. http://dx.doi.org/10.1017/s002211200800459x.
Анотація:
We have studied the temporal evolution of electro-kinetic flows in the vicinity of polarizable dielectric solids following the application of a ‘weak’ transient electric field. To obtain a macro-scale description in the limit of narrow electric double layers (EDLs), we have derived a pair of effective transient boundary conditions directly connecting the electric potentials across the EDL. Within the framework of the above assumptions, these conditions apply to a general transient electro-kinetic problem involving dielectric solids of arbitrary geometry and relative permittivity. Furthermore, the newly derived scheme is applicable to general transient and spatially non-uniform external fields. We examine the details of the physical mechanisms involved in the relaxation of the induced-charging process of the EDL adjacent to polarizable dielectric solids. It is thus established that the time scale characterizing the electrostatic relaxation increases with the dielectric constant of the solid from the Debye time (for the diffusion across the EDL) through the ‘intermediate’ scale (proportional to the product of the respective Debye- and geometric-length scales). Thus, the present rigorous analysis substantiates earlier results largely obtained by heuristic use of equivalent RC-circuit models. Furthermore, for typical values of ionic diffusivity and kinematic viscosity of the electrolyte solution, the latter time scale is comparable to the time scale of viscous relaxation in problems concerning microfluidic applications or micro-particle dynamics. The analysis is illustrated for spherical micro-particles. Explicit results are thus presented for the temporal evolution of electro-osmosis around a dielectric sphere immersed in unbounded electrolyte solution under the action of a suddenly applied uniform field, combining both induced charge and ‘equilibrium’ (fixed charge) contributions to the zeta potential. It is demonstrated that, owing to the time delay of the induced-EDL charging, the ‘equilibrium’ contribution to fluid motion (which is linear in the electric field) initially dominates the (quadratic) ‘induced’ contribution.
10
Lu, Jiachen, Negin Nazarian, Melissa Anne Hart, E. Scott Krayenhoff, and Alberto Martilli. "A one-dimensional urban flow model with an eddy-diffusivity mass-flux (EDMF) scheme and refined turbulent transport (MLUCM v3.0)." Geoscientific Model Development 17, no. 7 (April 5, 2024): 2525–45. http://dx.doi.org/10.5194/gmd-17-2525-2024.
Анотація:
Abstract. In recent years, urban canopy models (UCMs) have been used as fully coupled components of mesoscale atmospheric models as well as offline tools to estimate temperature and surface fluxes using atmospheric forcings. Examples include multi-layer urban canopy models (MLUCMs), where the vertical variability of turbulent fluxes is calculated by solving prognostic momentum and turbulent kinetic energy (TKE, k) using mixing length scale (l) and drag parameterizations. These parameterizations are based on the well-established 1.5-order k−l turbulence closure theory and are often informed by microscale fluid dynamics simulations. However, this approach can include simplifications such as assuming the same diffusion coefficient for momentum, TKE, and scalars. In addition, the dispersive stresses arising from spatially averaged flow properties have been parameterized together with the turbulent fluxes despite being controlled by different mechanisms. Both of these assumptions impact the quantification of the turbulent exchange of flow properties and subsequent air temperature predictions in urban canopies. To assess these assumptions and improve corresponding parameterization, we analyzed 49 large-eddy simulations (LES) for idealized urban arrays, encompassing variable building height distributions and a comprehensive range of urban densities (λp∈[0.0625,0.64]) seen in global cities. We find that the efficiency of turbulent transport (numerically described via diffusion coefficients) is similar for scalars and momentum but is 3.5 times higher for TKE. Additionally, parameterizing the dispersive momentum flux using the k−l closure was a source of error, while scaling with the pressure gradient and urban morphological parameters appears more appropriate. In response to these findings, we propose two changes to the previous version of MLUCM: (a) separate characterization for turbulent diffusion coefficient for momentum and TKE and (b) introduction of an explicit physics-based “mass-flux” term to represent the fraction of the dispersive momentum transport directly induced from buildings as an amendment to the existing “eddy-diffusivity” framework. The updated one-dimensional model, after being tuned for building height variability, is further compared against the original LES results and demonstrates improved performance in predicting vertical turbulent exchange in urban canopies.
11
Berkemeier, T., A. J. Huisman, M. Ammann, M. Shiraiwa, T. Koop, and U. Pöschl. "Kinetic regimes and limiting cases of gas uptake and heterogeneous reactions in atmospheric aerosols and clouds: a general classification scheme." Atmospheric Chemistry and Physics Discussions 13, no. 1 (January 9, 2013): 983–1044. http://dx.doi.org/10.5194/acpd-13-983-2013.
Анотація:
Abstract. Heterogeneous reactions are important to atmospheric chemistry and are therefore an area of intense research. In multiphase systems such as aerosols and clouds, chemical reactions are usually strongly coupled to a complex sequence of mass transport processes and results are often not easy to interpret. Here we present a systematic classification scheme for gas uptake by aerosol or cloud particles which distinguishes two major regimes: a reaction-diffusion regime and a mass-transfer regime. Each of these regimes includes four distinct limiting cases, characterized by a dominant reaction location (surface or bulk) and a single rate-limiting process: chemical reaction, bulk diffusion, gas-phase diffusion or mass accommodation. The conceptual framework enables efficient comparison of different studies and reaction systems, going beyond the scope of previous classification schemes by explicitly resolving interfacial transport processes and surface reactions limited by mass transfer from the gas phase. The use of kinetic multi-layer models instead of resistor model approaches increases the flexibility and enables a broader treatment of the subject, including cases which do not fit into the strict limiting cases typical of most resistor model formulations. The relative importance of different kinetic parameters such as diffusion, reaction rate and accommodation coefficients in this system is evaluated by a quantitative global sensitivity analysis. We outline the characteristic features of each limiting case and discuss the potential relevance of different regimes and limiting cases for various reaction systems. In particular, the classification scheme is applied to three different data sets for the benchmark system of oleic acid reacting with ozone. In light of these results, future directions of research needed to elucidate the multiphase chemical kinetics in this and other reaction systems are discussed.
12
Berkemeier, T., A. J. Huisman, M. Ammann, M. Shiraiwa, T. Koop, and U. Pöschl. "Kinetic regimes and limiting cases of gas uptake and heterogeneous reactions in atmospheric aerosols and clouds: a general classification scheme." Atmospheric Chemistry and Physics 13, no. 14 (July 15, 2013): 6663–86. http://dx.doi.org/10.5194/acp-13-6663-2013.
Анотація:
Abstract. Heterogeneous reactions are important to atmospheric chemistry and are therefore an area of intense research. In multiphase systems such as aerosols and clouds, chemical reactions are usually strongly coupled to a complex sequence of mass transport processes and results are often not easy to interpret. Here we present a systematic classification scheme for gas uptake by aerosol or cloud particles which distinguishes two major regimes: a reaction-diffusion regime and a mass transfer regime. Each of these regimes includes four distinct limiting cases, characterised by a dominant reaction location (surface or bulk) and a single rate-limiting process: chemical reaction, bulk diffusion, gas-phase diffusion or mass accommodation. The conceptual framework enables efficient comparison of different studies and reaction systems, going beyond the scope of previous classification schemes by explicitly resolving interfacial transport processes and surface reactions limited by mass transfer from the gas phase. The use of kinetic multi-layer models instead of resistor model approaches increases the flexibility and enables a broader treatment of the subject, including cases which do not fit into the strict limiting cases typical of most resistor model formulations. The relative importance of different kinetic parameters such as diffusion, reaction rate and accommodation coefficients in this system is evaluated by a quantitative global sensitivity analysis. We outline the characteristic features of each limiting case and discuss the potential relevance of different regimes and limiting cases for various reaction systems. In particular, the classification scheme is applied to three different datasets for the benchmark system of oleic acid reacting with ozone in order to demonstrate utility and highlight potential issues. In light of these results, future directions of research needed to elucidate the multiphase chemical kinetics in this and other reaction systems are discussed.
13
Artichowicz, Wojciech, and Dariusz Gąsiorowski. "Computationally Efficient Solution of a 2D Diffusive Wave Equation Used for Flood Inundation Problems." Water 11, no. 10 (October 22, 2019): 2195. http://dx.doi.org/10.3390/w11102195.
Анотація:
This paper presents a study dealing with increasing the computational efficiency in modeling floodplain inundation using a two-dimensional diffusive wave equation. To this end, the domain decomposition technique was used. The resulting one-dimensional diffusion equations were approximated in space with the modified finite element scheme, whereas time integration was carried out using the implicit two-level scheme. The proposed algorithm of the solution minimizes the numerical errors and is unconditionally stable. Consequently, it is possible to perform computations with a significantly greater time step than in the case of the explicit scheme. An additional efficiency improvement was achieved using the symmetry of the tridiagonal matrix of the arising system of nonlinear equations, due to the application of the parallelization strategy. The computational experiments showed that the proposed parallel implementation of the implicit scheme is very effective, at about two orders of magnitude with regard to computational time, in comparison with the explicit one.
14
Zhang, Chunyan, and Yuanyang Qiao. "Radial Basis Function–Finite Difference Solution Combined with Level-Set Embedded Boundary Method for Improving a Diffusive Logistic Model with a Free Boundary." Axioms 13, no. 4 (March 25, 2024): 217. http://dx.doi.org/10.3390/axioms13040217.
Анотація:
In this paper, we propose an efficient numerical method to solve the problems of diffusive logistic models with free boundaries, which are often used to simulate the spreading of new or invasive species. The boundary movement is tracked by the level-set method, where the Hamilton–Jacobi weighted essentially nonoscillatory (HJ-WENO) scheme is utilized to capture the boundary curve embedded by the Cartesian grids via the embedded boundary method. Then the radial basis function–finite difference (RBF-FD) method is adopted for spatial discretization and the implicit–explicit (IMEX) scheme is considered for time integration. A variety of numerical examples are utilized to demonstrate the evolution of the diffusive logistic model with different initial boundaries.
15
Jiang, Yao-Lin, and Yun-Bo Yang. "Semi-Discrete Galerkin Finite Element Method for the Diffusive Peterlin Viscoelastic Model." Computational Methods in Applied Mathematics 18, no. 2 (April 1, 2018): 275–96. http://dx.doi.org/10.1515/cmam-2017-0021.
Анотація:
AbstractIn this paper, a semi-discrete Galerkin finite element method is applied to the two-dimensional diffusive Peterlin viscoelastic model which can describe the unsteady behavior of some incompressible ploymeric fluids. For the derived semi-discrete finite element spatial discretization scheme, the a priori bounds are given that does not rely on the mesh width restriction. Further, with the help of the a priori error bounds of the Stokes and Ritz projections, optimal error estimates for the velocity, the conformation tensor and the pressure are presented, respectively. Finally, in order to implement the proposed semi-discrete numerical scheme, we derive three kinds of fully discrete schemes, e.g., Newton’s iterative scheme, Picard’s iterative scheme and implicit-explicit time-stepping scheme. Finally, several numerical experiments are conducted to confirm our theoretical results.
16
Retsinis, Eugene, Erna Daskalaki, and Panayiotis Papanicolaou. "Dynamic flood wave routing in prismatic channels with hydraulic and hydrologic methods." Journal of Water Supply: Research and Technology-Aqua 69, no. 3 (October 23, 2019): 276–87. http://dx.doi.org/10.2166/aqua.2019.091.
Анотація:
Abstract Time-dependent, unsteady flow has been studied in prismatic open channels with symmetric trapezoidal and triangular cross sections and small bottom slope. The St Venant equations without lateral inflow have been discretized in explicit as well as in implicit form and solved numerically, for unsteady, subcritical flow. The inflow hydrograph used can be applied for different flood events by adjusting its parameters accordingly. The results presented are derived from the explicit schemes Lax-Diffusive, MacCormack, Lambda as well as the implicit Preissmann scheme, and are compared to those from the Muskingum-Cunge method and the widely used commercial software HEC-RAS. The peak flow computed by the Lax-Diffusive scheme was reduced at the downstream end of the channel and the arrival time of the peak increased if compared to the other methods. The Muskingun-Cunge method forecasted the shortest peak flow arrival time at the downstream end cross section. Mass conservation computed from inflow and outflow hydrographs has been confirmed, since the maximum error did not exceed 2.60%. All codes were implemented in house using Matlab®.
17
Boscarino, S., L. Pareschi, and G. Russo. "Implicit-Explicit Runge--Kutta Schemes for Hyperbolic Systems and Kinetic Equations in the Diffusion Limit." SIAM Journal on Scientific Computing 35, no. 1 (January 2013): A22—A51. http://dx.doi.org/10.1137/110842855.
18
Moschetta, Jean-Marc, and D. I. Pullin. "A Robust Low Diffusive Kinetic Scheme for the Navier–Stokes/Euler Equations." Journal of Computational Physics 133, no. 2 (May 1997): 193–204. http://dx.doi.org/10.1006/jcph.1997.5673.
19
Marcinkevicius, Romas, Inga Telksniene, Tadas Telksnys, Zenonas Navickas, and Minvydas Ragulskis. "The step-wise construction of solitary solutions to Riccati equations with diffusive coupling." AIMS Mathematics 8, no. 12 (2023): 30683–703. http://dx.doi.org/10.3934/math.20221568.
Анотація:
<abstract><p>A novel scheme based on the generalized differential operator and computer algebra was used to construct solitary solutions to a system of Riccati differential equations with diffusive coupling. The presented approach yields necessary and sufficient existence conditions of solitary solutions with respect to the system parameters. The proposed stepwise approach enabled the derivation of the explicit analytic solution, which could not be derived using direct balancing techniques due to the complexity of algebraic relationships. Computational experiments were used to demonstrate the efficacy of proposed scheme.</p></abstract>
20
Marcinkevicius, Romas, Inga Telksniene, Tadas Telksnys, Zenonas Navickas, and Minvydas Ragulskis. "The step-wise construction of solitary solutions to Riccati equations with diffusive coupling." AIMS Mathematics 8, no. 12 (2023): 30683–703. http://dx.doi.org/10.3934/math.20231568.
Анотація:
<abstract><p>A novel scheme based on the generalized differential operator and computer algebra was used to construct solitary solutions to a system of Riccati differential equations with diffusive coupling. The presented approach yields necessary and sufficient existence conditions of solitary solutions with respect to the system parameters. The proposed stepwise approach enabled the derivation of the explicit analytic solution, which could not be derived using direct balancing techniques due to the complexity of algebraic relationships. Computational experiments were used to demonstrate the efficacy of proposed scheme.</p></abstract>
21
Seaïd, Mohammed. "On the Quasi-monotone Modified Method of Characteristics for Transport-diffusion Problems with Reactive Sources." Computational Methods in Applied Mathematics 2, no. 2 (2001): 186–210. http://dx.doi.org/10.2478/cmam-2002-0012.
Анотація:
AbstractThis is an attempt to construct a strong numerical method for transportdiffusion equations with nonlinear reaction terms, which relies on the idea of the Modified Method of Characteristics that is explicit but stable and is second-order accurate in time. The method consists in convective-diffusive splitting of the equations along the characteristics. The convective stage of the splitting is straightforwardly treated by a quasi-monotone and conservative modified method of characteristics, while the diffusive-reactive stage can be approximated by an explicit scheme with an extended real stability interval. A numerical comparative study of the new method with Characteristics Crank-Nicholson and Classical Characteristics Runge-Kutta schemes, which are used in many transport-diffusion models, is carried out for several benchmark problems, whose solutions represent relevant transport-diffusion-reaction features. Experiments for transport-diffusion equations with linear and nonlinear reactive sources demonstrate the ability of our new algorithm to better maintain the shape of the solution in the presence of shocks and discontinuities.
22
Carrillo, José A., and Bokai Yan. "An Asymptotic Preserving Scheme for the Diffusive Limit of Kinetic Systems for Chemotaxis." Multiscale Modeling & Simulation 11, no. 1 (January 2013): 336–61. http://dx.doi.org/10.1137/110851687.
23
Galeazzo, Tommaso, Richard Valorso, Ying Li, Marie Camredon, Bernard Aumont та Manabu Shiraiwa. "Estimation of secondary organic aerosol viscosity from explicit modeling of gas-phase oxidation of isoprene and <i>α</i>-pinene". Atmospheric Chemistry and Physics 21, № 13 (7 липня 2021): 10199–213. http://dx.doi.org/10.5194/acp-21-10199-2021.
Анотація:
Abstract. Secondary organic aerosols (SOA) are major components of atmospheric fine particulate matter, affecting climate and air quality. Mounting evidence exists that SOA can adopt glassy and viscous semisolid states, impacting formation and partitioning of SOA. In this study, we apply the GECKO-A (Generator of Explicit Chemistry and Kinetics of Organics in the Atmosphere) model to conduct explicit chemical modeling of isoprene photooxidation and α-pinene ozonolysis and their subsequent SOA formation. The detailed gas-phase chemical schemes from GECKO-A are implemented into a box model and coupled to our recently developed glass transition temperature parameterizations, allowing us to predict SOA viscosity. The effects of chemical composition, relative humidity, mass loadings and mass accommodation on particle viscosity are investigated in comparison with measurements of SOA viscosity. The simulated viscosity of isoprene SOA agrees well with viscosity measurements as a function of relative humidity, while the model underestimates viscosity of α-pinene SOA by a few orders of magnitude. This difference may be due to missing processes in the model, including autoxidation and particle-phase reactions, leading to the formation of high-molar-mass compounds that would increase particle viscosity. Additional simulations imply that kinetic limitations of bulk diffusion and reduction in mass accommodation coefficient may play a role in enhancing particle viscosity by suppressing condensation of semi-volatile compounds. The developed model is a useful tool for analysis and investigation of the interplay among gas-phase reactions, particle chemical composition and SOA phase state.
24
Arif, Muhammad Shoaib, Kamaleldin Abodayeh, and Asad Ejaz. "On the stability of the diffusive and non-diffusive predator-prey system with consuming resources and disease in prey species." Mathematical Biosciences and Engineering 20, no. 3 (2023): 5066–93. http://dx.doi.org/10.3934/mbe.2023235.
Анотація:
<abstract> <p>This research deals with formulating a multi-species eco-epidemiological mathematical model when the interacting species compete for the same food sources and the prey species have some infection. It is assumed that infection does not spread vertically. Infectious diseases severely affect the population dynamics of prey and predator. One of the most important factors in population dynamics is the movement of species in the habitat in search of resources or protection. The ecological influences of diffusion on the population density of both species are studied. The study also deals with the analysis of the effects of diffusion on the fixed points of the proposed model. The fixed points of the model are sorted out. The Lyapunov function is constructed for the proposed model. The fixed points of the proposed model are analyzed through the use of the Lyapunov stability criterion. It is proved that coexisting fixed points remain stable under the effects of self-diffusion, whereas, in the case of cross-diffusion, Turing instability exists conditionally. Moreover, a two-stage explicit numerical scheme is constructed, and the stability of the said scheme is found by using von Neumann stability analysis. Simulations are performed by using the constructed scheme to discuss the model's phase portraits and time-series solution. Many scenarios are discussed to display the present study's significance. The impacts of the transmission parameter 𝛾 and food resource <italic>f</italic> on the population density of species are presented in plots. It is verified that the availability of common food resources greatly influences the dynamics of such models. It is shown that all three classes, i.e., the predator, susceptible prey and infected prey, can coexist in the habitat, and this coexistence has a stable nature. Hence, in the realistic scenarios of predator-prey ecology, the results of the study show the importance of food availability for the interacting species.</p> </abstract>
25
Wang, Dean, and Zuolong Zhu. "A Revisit to CMFD Schemes: Fourier Analysis and Enhancement." Energies 14, no. 2 (January 14, 2021): 424. http://dx.doi.org/10.3390/en14020424.
Анотація:
The coarse-mesh finite difference (CMFD) scheme is a very effective nonlinear diffusion acceleration method for neutron transport calculations. CMFD can become unstable and fail to converge when the computational cell optical thickness is relatively large in k-eigenvalue problems or diffusive fixed-source problems. Some variants and fixups have been developed to enhance the stability of CMFD, including the partial current-based CMFD (pCMFD), optimally diffusive CMFD (odCMFD), and linear prolongation-based CMFD (lpCMFD). Linearized Fourier analysis has proven to be a very reliable and accurate tool to investigate the convergence rate and stability of such coupled high-order transport/low-order diffusion iterative schemes. It is shown in this paper that the use of different transport solvers in Fourier analysis may have some potential implications on the development of stabilizing techniques, which is exemplified by the odCMFD scheme. A modification to the artificial diffusion coefficients of odCMFD is proposed to improve its stability. In addition, two explicit expressions are presented to calculate local optimal successive overrelaxation (SOR) factors for lpCMFD to further enhance its acceleration performance for fixed-source problems and k-eigenvalue problems, respectively.
26
Oishi, C. M., J. A. Cuminato, V. G. Ferreira, M. F. Tomé, A. Castelo, and N. Mangiavacchi. "A SEMI-IMPLICIT SCHEME FOR SOLVING INCOMPRESSIBLE VISCOUS FREE SURFACE FLOWS." Revista de Engenharia Térmica 4, no. 2 (December 31, 2005): 106. http://dx.doi.org/10.5380/reterm.v4i2.5406.
Анотація:
The present work is concerned with a numerical method for solving the two-dimensional time-dependent incompressible Navier-Stokes equations in the primitive variables formulation. The diffusive terms are treated by Implicit Backward and Crank-Nicolson methods, and the non-linear convection terms are, explicitly, approximated by the high order upwind VONOS (Variable-Order Non-Oscillatory Scheme) scheme. The boundary conditions for the pressure field at the free surface are treated implicitly, and for the velocity field explicitly. The numerical method is then applied to the simulation of free surface and confined flows. The numerical results show that the present technique eliminates the stability restriction in the original explicit method. For low Reynolds number flow dynamics, the method is robust and produces numerical results that compare very well with the analytical solutions.
27
Sun, Wenjun, Song Jiang, and Kun Xu. "An Implicit Unified Gas Kinetic Scheme for Radiative Transfer with Equilibrium and Non-Equilibrium Diffusive Limits." Communications in Computational Physics 22, no. 4 (July 28, 2017): 889–912. http://dx.doi.org/10.4208/cicp.oa-2016-0261.
Анотація:
AbstractThis paper is about the construction of a unified gas-kinetic scheme (UGKS) for a coupled system of radiative transport and material heat conduction with different diffusive limits. Different from the previous approach, instead of including absorption/emission only, the current method takes both scattering and absorption/emission mechanism into account in the radiative transport process. As a result, two asymptotic limiting solutions will appear in the diffusive regime. In the strong absorption/emission case, an equilibrium diffusion limit is obtained, where the system is mainly driven by a nonlinear diffusion equation for the equilibrium radiation and material temperature. However, in the strong scattering case, a non-equilibrium limit can be obtained, where coupled nonlinear diffusion system with different radiation and material temperature is obtained. In addition to including the scattering term in the transport equation, an implicit UGKS (IUGKS) will be developed in this paper as well. In the IUGKS, the numerical flux for the radiation intensity is constructed implicitly. Therefore, the conventional CFL constraint for the time step is released. With the use of a large time step for the radiative transport, it becomes possible to couple the IUGKS with the gas dynamic equations to develop an efficient numerical method for radiative hydrodynamics. The IUGKS is a valid method for all radiative transfer regimes. A few numerical examples will be presented to validate the current implicit method for both optical thin to optical thick cases.
28
Bretti, Gabriella, Laurent Gosse, and Nicolas Vauchelet. "Diffusive limits of 2D well-balanced schemes for kinetic models of neutron transport." ESAIM: Mathematical Modelling and Numerical Analysis 55, no. 6 (November 2021): 2949–80. http://dx.doi.org/10.1051/m2an/2021077.
Анотація:
Two-dimensional dissipative and isotropic kinetic models, like the ones used in neutron transport theory, are considered. Especially, steady-states are expressed for constant opacity and damping, allowing to derive a scattering S-matrix and corresponding "truly 2D well-balanced" numerical schemes. A first scheme is obtained by directly implementing truncated Fourier–Bessel series, whereas another proceeds by applying an exponential modulation to a former, conservative, one. Consistency with the asymptotic damped parabolic approximation is checked for both algorithms. A striking property of some of these schemes is that they can be proved to be both 2D well-balanced and asymptotic-preserving in the parabolic limit, even when setting up IMEX time-integrators: see Corollaries 3.4 and A.1. These findings are further confirmed by means of practical benchmarks carried out on coarse Cartesian computational grids.
29
Häfliger, Vincent, Eric Martin, Aaron Boone, Florence Habets, Cédric H. David, Pierre-A. Garambois, Hélène Roux, et al. "Evaluation of Regional-Scale River Depth Simulations Using Various Routing Schemes within a Hydrometeorological Modeling Framework for the Preparation of the SWOT Mission." Journal of Hydrometeorology 16, no. 4 (July 29, 2015): 1821–42. http://dx.doi.org/10.1175/jhm-d-14-0107.1.
Анотація:
Abstract The Surface Water and Ocean Topography (SWOT) mission will provide free water surface elevations, slopes, and river widths for rivers wider than 50 m. Models must be prepared to use this new finescale information by explicitly simulating the link between runoff and the river channel hydraulics. This study assesses one regional hydrometeorological model’s ability to simulate river depths. The Garonne catchment in southwestern France (56 000 km2) has been chosen for the availability of operational gauges in the river network and finescale hydraulic models over two reaches of the river. Several routing schemes, ranging from the simple Muskingum method to time-variable parameter kinematic and diffusive waves schemes, are tested. The results show that the variable flow velocity schemes are advantageous for discharge computations when compared to the original Muskingum routing method. Additionally, comparisons between river depth computations and in situ observations in the downstream Garonne River led to root-mean-square errors of 50–60 cm in the improved Muskingum method and 40–50 cm in the kinematic–diffusive wave method. The results also highlight SWOT’s potential to improve the characterization of hydrological processes for subbasins larger than 10 000 km2, the importance of an accurate digital elevation model, and the need for spatially varying hydraulic parameters.
30
Abgrall, Rémi, and Davide Torlo. "Some preliminary results on a high order asymptotic preserving computationally explicit kinetic scheme." Communications in Mathematical Sciences 20, no. 2 (2022): 297–326. http://dx.doi.org/10.4310/cms.2022.v20.n2.a1.
31
Shutts, G. J. "Coarse Graining the Vorticity Equation in the ECMWF Integrated Forecasting System: The Search for Kinetic Energy Backscatter." Journal of the Atmospheric Sciences 70, no. 4 (April 1, 2013): 1233–41. http://dx.doi.org/10.1175/jas-d-12-0216.1.
Анотація:
Abstract Stochastic kinetic energy backscatter parameterization schemes are now widely used in ensemble prediction systems to account for random error associated with excessive dissipation and unrepresented energy backscatter in numerical weather prediction models. This dissipation arises from numerical advection schemes and explicit diffusion terms and is also implicit in some parameterization schemes. In the absence of a backscatter theory applicable to the convective scale and mesoscale, current parameterization methods are based on simple heuristic models designed to scale the energy input in proportion to a suitable measure of net energy dissipation rate. Free parameters in the formulation of backscatter tend to be tuned for the optimal performance of ensemble prediction systems, yet other forms of uncertainty represented in these forecasting systems make that task harder. Results are presented here from a study that aims to characterize the form and magnitude of kinetic energy backscatter within a global spectral framework. This is achieved by comparing a high-resolution “truth” model with a spectrally truncated version of the model for which the effect of the missing scales of motion is to be gauged. Energy exchange between these omitted scales and the resolved scales of the truncated representation is computed for the dominant terms in the vorticity equation. It is found that although there is a nonlocal spectral energy flux to low wavenumbers due to the purely rotational part of the flow, it is much smaller than the dissipative effect associated with terms involving the divergent part of the flow. Biharmonic horizontal diffusion is found to contribute significantly as an energy sink across the entire wavenumber spectrum.
32
Salama, Fouad Mohammad, and Faisal Fairag. "On numerical solution of two-dimensional variable-order fractional diffusion equation arising in transport phenomena." AIMS Mathematics 9, no. 1 (2024): 340–70. http://dx.doi.org/10.3934/math.2024020.
Анотація:
<abstract><p>In recent years, the application of variable-order (VO) fractional differential equations for describing complex physical phenomena ranging from biology, hydrology, mechanics and viscoelasticity to fluid dynamics has become one of the most hot topics in the context of scientific modeling. An interesting aspect of VO operators is their capability to address the behavior of scientific and engineering systems with time and spatially varying properties. The VO fractional diffusion equation is a fundamental model that allows transitions among sub-diffusive, diffusive and super-diffusive behaviors without altering the underlying governing equations. In this paper, we considered the two-dimensional fractional diffusion equation with the Caputo time VO derivative, which is essential for describing anomalous diffusion in real-world complex systems. A new Crank-Nicolson (C-N) difference scheme and an efficient explicit decoupled group (EDG) method were proposed to solve the problem under consideration. The proposed EDG method is based on a skewed difference scheme in conjunction with a grouping procedure of the solution grid points. Special attention was devoted to investigating the stability and convergence of the proposed methods. Three numerical examples with known exact analytical solutions were provided to illustrate our considerations. The proposed methods were shown to be stable and convergent theoretically as well as numerically. In addition, a comparative study was done between the EDG method and the C-N difference scheme. It was found that the proposed methods are accurate in simulating the considered problem, while the EDG method is superior to the C-N difference method in terms of Central Processing Unit (CPU) timing, verifying the efficiency of the former method in solving the VO problem.</p></abstract>
33
Yang, X., Y. Tang, D. Cai, L. Zhang, Y. Du, and S. Zhou. "Comparative analysis of different numerical schemes in solute trapping simulations by using the phase-field model with finite interface dissipation." Journal of Mining and Metallurgy, Section B: Metallurgy 52, no. 1 (2016): 77–85. http://dx.doi.org/10.2298/jmmb150716010y.
Анотація:
Two different numerical schemes, the standard explicit scheme and the time-elimination relaxation one, in the framework of phase-field model with finite interface dissipation were employed to investigate the solute trapping effect in a Si-4.5 at.% As alloy during rapid solidification. With the equivalent input, a unique solute distribution under the steady state can be obtained by using the two schemes without restriction to numerical length scale and interface velocity. By adjusting interface width and interface permeability, the experimental solute segregation coefficients can be well reproduced. The comparative analysis of advantages and disadvantages in the two numerical schemes indicates that the time-elimination relaxation scheme is preferable in one-dimensional phase-field simulation, while the standard explicit scheme seems to be the only choice for two- or three dimensional phase-field simulation. Furthermore, the kinetic phase diagrams in the Si-As system were predicted by using the phase-field simulation with the time-elimination relaxation scheme.
34
SUZUKI, KOSUKE, and TAKAJI INAMURO. "AN IMPROVED LATTICE KINETIC SCHEME FOR INCOMPRESSIBLE VISCOUS FLUID FLOWS." International Journal of Modern Physics C 25, no. 01 (December 2, 2013): 1340017. http://dx.doi.org/10.1142/s0129183113400172.
Анотація:
The lattice Boltzmann method (LBM) is an explicit numerical scheme for the incompressible Navier–Stokes equations (INSE) without integrating the Poisson equation for the pressure. In spite of its merit, the LBM has some drawbacks in accuracy. First, we review drawbacks for three numerical methods based on the LBM. The three methods are the LBM with the Bhatnagar–Gross–Krook model (LBGK), the lattice kinetic scheme (LKS) and the link-wise artificial compressibility method (LWACM). Second, in order to remedy the drawbacks, we propose an improved LKS. The present method incorporates (i) the scheme used in the LWACM for determining the kinematic viscosity, (ii) an iterative calculation of the pressure and (iii) a semi-implicit algorithm, while preserving the simplicity of the algorithm of the original LKS. Finally, in simulations of test problems, we find that the improved LKS eliminates the drawbacks and gives more accurate and stable results than LBGK, LKS and LWACM.
35
Hochbruck, Marlis, and Jan Leibold. "An implicit–explicit time discretization scheme for second-order semilinear wave equations with application to dynamic boundary conditions." Numerische Mathematik 147, no. 4 (March 3, 2021): 869–99. http://dx.doi.org/10.1007/s00211-021-01184-w.
Анотація:
AbstractWe construct and analyze a second-order implicit–explicit (IMEX) scheme for the time integration of semilinear second-order wave equations. The scheme treats the stiff linear part of the problem implicitly and the nonlinear part explicitly. This makes the scheme unconditionally stable and at the same time very efficient, since it only requires the solution of one linear system of equations per time step. For the combination of the IMEX scheme with a general, abstract, nonconforming space discretization we prove a full discretization error bound. We then apply the method to a nonconforming finite element discretization of an acoustic wave equation with a kinetic boundary condition. This yields a fully discrete scheme and a corresponding a-priori error estimate.
36
Garrido, P. L. "Quasipotentials in the nonequilibrium stationary states or a method to get explicit solutions of Hamilton–Jacobi equations." Journal of Statistical Mechanics: Theory and Experiment 2021, no. 11 (November 1, 2021): 113206. http://dx.doi.org/10.1088/1742-5468/ac382d.
Анотація:
Abstract We assume that a system at a mesoscopic scale is described by a field ϕ(x, t) that evolves by a Langevin equation with a white noise whose intensity is controlled by a parameter 1 / Ω . The system stationary state distribution in the small noise limit (Ω → ∞) is of the form P st [ϕ] ≃ exp(−ΩV 0[ϕ]), where V 0[ϕ] is called the quasipotential. V 0 is the unknown of a Hamilton–Jacobi equation. Therefore, V 0 can be written as an action computed along a path that is the solution from Hamilton’s equation that typically cannot be solved explicitly. This paper presents a theoretical scheme that builds a suitable canonical transformation that permits us to do such integration by deforming the original path into a straight line and including some weights along with it. We get the functional form of such weights through conditions on the existence and structure of the canonical transformation. We apply the scheme to get the quasipotential algebraically for several one-dimensional nonequilibrium models as the diffusive and reaction–diffusion systems.
37
Nagy, Endre, and Imre Hegedüs. "Diffusive Plus Convective Mass Transport, Accompanied by Biochemical Reaction, Across Capillary Membrane." Catalysts 10, no. 10 (September 25, 2020): 1115. http://dx.doi.org/10.3390/catal10101115.
Анотація:
This study theoretically analyzes the mass transport through capillary, asymmetric, biocatalytic membrane reactor, where the diffusive plus convective mass transport is accompanied by biochemical reaction with Michaelis-Menten kinetics. An approach mathematical model was developed that provides the mass transfer properties in closed, explicit mathematical forms. The inlet and outlet mass transfer rates can then put into the differential mass transport expressions of the lumen and the shell fluid phases as boundary values. The approach solution was obtained by dividing the membrane layer into very thin sub-layers with constant transport and reaction kinetic parameters and the obtained second-order differential equation with constant parameters, given for every sublayer, could be solved analytically. Two operating modes are analyzed in this paper, namely, with and without a sweeping phase on the permeating side. These models deviate by the boundary conditions, only, defined them for the outlet membrane surface. The main purpose of this study is to show how the cylindrical space affects the transport process, concentration distribution, mass transfer rates and conversion in presence of a biochemical reaction. It is shown that the capillary transport can significantly be affected by the lumen radius, by the biocatalytic reactor thickness and the convective flow. Decreasing values of the lumen radius reduce the effect of the biochemical/chemical reaction; the increasing reactor thickness also decreases the physical mass transfer rate and, with it, increases the effect of reaction rate. The model can also be applied to reactions with more general kinetic equations with variable parameters.
38
Saha Ray, S., and A. Patra. "An Explicit Finite Difference scheme for numerical solution of fractional neutron point kinetic equation." Annals of Nuclear Energy 41 (March 2012): 61–66. http://dx.doi.org/10.1016/j.anucene.2011.11.006.
39
Lenz, Stephan, Martin Geier, and Manfred Krafczyk. "An explicit gas kinetic scheme algorithm on non-uniform Cartesian meshes for GPGPU architectures." Computers & Fluids 186 (May 2019): 58–73. http://dx.doi.org/10.1016/j.compfluid.2019.04.011.
40
Bondesan, Andrea, Laurent Boudin, and Bérénice Grec. "A numerical scheme for a kinetic model for mixtures in the diffusive limit using the moment method." Numerical Methods for Partial Differential Equations 35, no. 3 (January 17, 2019): 1184–205. http://dx.doi.org/10.1002/num.22345.
41
Rosero Chicaíza, David Camilo, and Bibian A. Hoyos. "Reaction kinetic parameters for a distributed model of transport and reaction in Pd/Rh/CeZrO three-way catalytic converters." DYNA 86, no. 210 (July 1, 2019): 216–23. http://dx.doi.org/10.15446/dyna.v86n210.78596.
Анотація:
This paper presents a two-dimensional distributed model for the transport and reaction of combustion gases in channels of three-way catalytic converters, considering a detailed reaction kinetics with 16 chemical reactions in palladium and rhodium catalysts, and taking into account diffusive effects within the coating, to obtain a new set of reaction kinetic parameters that do not depend on the thickness of the coating. The model was solved using a finite volume method with a first order upwind scheme and simulations were conducted using computational fluid dynamics. The model with the new distributed reaction kinetic parameters, produced an excellent agreement with the experimental data of concentration at the end of the channels. Also, the model reproduced the most important concentration changes for the gas components in the specified temperature range and allowed simulations with excess oxygen and different thicknesses.
42
Catureba, Rafaela Pedroso, Aldelio Bueno Caldeira, and Rodrigo Otávio de Castro Guedes. "Numerical Simulation of the TNT Solidification Process." Defence Science Journal 69, no. 4 (July 15, 2019): 336–41. http://dx.doi.org/10.14429/dsj.69.13536.
Анотація:
The solidification phenomenon is present in the casting process of energetic materials. In defence industry, trinitrotoluene (TNT) is used as main charge for high explosive ammunitions. The present study tackles the numerical simulation of the solidification process of TNT by means of a two-dimensional transient model in cylindrical coordinates. The heat conduction problem is solved by using the enthalpy method that rewrites the governing equation in terms of this variable. The transient diffusive equation is then numerically solved by applying finite volumes in an explicit scheme. The analysis the mold thickness and the convective boundary conditions are analysed to assess how they affect heat transfer during solidification. Results obtained allow for a better comprehension of this type of problem.
43
MIEUSSENS, LUC. "DISCRETE VELOCITY MODEL AND IMPLICIT SCHEME FOR THE BGK EQUATION OF RAREFIED GAS DYNAMICS." Mathematical Models and Methods in Applied Sciences 10, no. 08 (November 2000): 1121–49. http://dx.doi.org/10.1142/s0218202500000562.
Анотація:
We present a numerical method for computing transitional flows as described by the BGK equation of gas kinetic theory. Using the minimum entropy principle to define a discrete equilibrium function, a discrete velocity model of this equation is proposed. This model, like the continuous one, ensures positivity of solutions, conservation of moments, and dissipation of entropy. The discrete velocity model is then discretized in space and time by an explicit finite volume scheme which is proved to satisfy the previous properties. A linearized implicit scheme is then derived to efficiently compute steady-states; this method is then verified with several test cases.
44
Furter, J. E., and J. López-Gómez. "Diffusion-mediated permanence problem for a heterogeneous Lotka–Volterra competition model." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 127, no. 2 (1997): 281–336. http://dx.doi.org/10.1017/s0308210500023659.
Анотація:
We analyse the dynamics of a prototype model for competing species with diffusion coefficients (d1d2) in a heterogeneous environment Ω. When diffusion is switched off, at each point x ∊ Ω we have a pair of ODE's: the kinetic. If for some x ∊ Ω kinetic has a unique stable coexistence state, we show that there exist such that for every the RD-model is persistent, in the sense that it has a compact global attractor within the interior of the positive cone and has a stable coexistence state. The same result is true if there exist xu, xv ∊ Ω such that the semitrivial coexistence states (u, 0) and (0, v) of the kinetic are globally asymptotically stable at x = xu and x = xv, respectively. More generally, our main result shows that, for most kinetic patterns, stable coexistence of xspopulations can be found for some range of the diffusion coefficients.Singular perturbation techniques, monotone schemes, fixed point index, global analysis of persistence curves, global continuation and singularity theory are some of the technical tools employed to get the previous results, among others. These techniques give us necessary and/or sufficient conditions for the existence and uniqueness of coexistence states, conditions which can be explicitly evaluated by estimating some principal eigenvalues of certain elliptic operators whose coefficients are solutions of semilinear boundary value problems.We also discuss counterexamples to the necessity of the sufficient conditions through the analysis of the local bifurcations from the semitrivial coexistence states at the principal eigenvalues. An easy consequence of our analysis is the existence of models having exactly two coexistence states, one of them stable and the other one unstable. We find that there are also cases for which the model has three or more coexistence states.
45
Abarca, A., M. Avramova, K. Ivanov, S. Verdebout, D. De Meyer, and C. R. Schneidesch. "DEVELOPMENT AND VERIFICATION OF T-TRACE/PANTHER COUPLED CODE." EPJ Web of Conferences 247 (2021): 06027. http://dx.doi.org/10.1051/epjconf/202124706027.
Анотація:
Multi-physics coupled simulations have become increasingly important during the last two decades being one of the major field of application in the nuclear technology. The nuclear reactors themselves are complex systems whose responses are driven by interactions between neutron kinetics, thermal-hydraulics, heat transfer, mechanics and chemistry. Probably, in a nuclear system, the most complex and important feedback effect takes place between the core neutron kinetics and thermal-hydraulics. The development of coupled thermal-hydraulic -neutron kinetics codes is a recurrent field of research for the nuclear industry. This contribution, developed in the Consortium for Nuclear Power (CNP) framework, has the objective of develop a dynamic coupling, using TCP/IP based socket communication, between the thermal-hydraulic system code T-TRACE, Tractebel-ENGIE version of the latest US NRC TRACE release, and the multi-group 3-D nodal diffusion and core physics code PANTHER, developed and maintained by EDF Energy (UK). As a first step of the development, a fully temporally explicit coupling scheme has been developed between TRACE and PANTHER based on a boundary conditions exchange at the core level at each temporal iteration. The OECD TMI MSLB benchmark has been selected as verification scenario for testing the ongoing developing T-TRACE/PANTHER coupled code. The developed coupled code is benchmarked code-to-code against TRACE/PARCS and T-RELAP5/PANTHER.
46
Chamkha, Ali J., M. F. Al-Amin, and Abdelraheem Aly. "Unsteady double-diffusive natural convective MHD flow along a vertical cylinder in the presence of chemical reaction, thermal radiation and Soret and Dufour effects." Journal of Naval Architecture and Marine Engineering 8, no. 1 (June 1, 2011): 25–36. http://dx.doi.org/10.3329/jname.v8i1.7250.
Анотація:
This work is focused on the numerical solution of unsteady double-diffusive free convective flow along a vertical isothermal cylinder in the presence of a transverse magnetic field, first-order homogeneous chemical reaction, thermal radiation and Soret and Dufour effects. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing equations are formulated and a numerical solution is obtained by using an explicit finite-difference scheme. The solutions at each time step have been found to reach the steady state solution properly. Representative results for the fluid velocity, temperature and solute concentration profiles as well as the local heat and mass transfer rates for various values of the physical parameters are displayed in both graphical and tabular forms. DOI: http://dx.doi.org/10.3329/jname.v8i1.7250
47
Wyss, Alejandra, and Arturo Hidalgo. "Modeling COVID-19 Using a Modified SVIR Compartmental Model and LSTM-Estimated Parameters." Mathematics 11, no. 6 (March 16, 2023): 1436. http://dx.doi.org/10.3390/math11061436.
Анотація:
This article presents a modified version of the SVIR compartmental model for predicting the evolution of the COVID-19 pandemic, which incorporates vaccination and a saturated incidence rate, as well as piece-wise time-dependent parameters that enable self-regulation based on the epidemic trend. We have established the positivity of the ODE version of the model and explored its local stability. Artificial neural networks are used to estimate time-dependent parameters. Numerical simulations are conducted using a fourth-order Runge–Kutta numerical scheme, and the results are compared and validated against actual data from the Autonomous Communities of Spain. The modified model also includes explicit parameters to examine potential future scenarios. In addition, the modified SVIR model is transformed into a system of one-dimensional PDEs with diffusive terms, and solved using a finite volume framework with fifth-order WENO reconstruction in space and an RK3-TVD scheme for time integration. Overall, this work demonstrates the effectiveness of the modified SVIR model and its potential for improving our understanding of the COVID-19 pandemic and supporting decision-making in public health.
48
Lutsko, Christopher, and Bálint Tóth. "Invariance Principle for the Random Lorentz Gas—Beyond the Boltzmann-Grad Limit." Communications in Mathematical Physics 379, no. 2 (September 16, 2020): 589–632. http://dx.doi.org/10.1007/s00220-020-03852-8.
Анотація:
Abstract We prove the invariance principle for a random Lorentz-gas particle in 3 dimensions under the Boltzmann-Grad limit and simultaneous diffusive scaling. That is, for the trajectory of a point-like particle moving among infinite-mass, hard-core, spherical scatterers of radius r, placed according to a Poisson point process of density $$\varrho $$ ϱ , in the limit $$\varrho \rightarrow \infty $$ ϱ → ∞ , $$r\rightarrow 0$$ r → 0 , $$\varrho r^{2}\rightarrow 1$$ ϱ r 2 → 1 up to time scales of order $$T=o(r^{-2}\left| {\log r}\right| ^{-2})$$ T = o ( r - 2 log r - 2 ) . To our knowledge this represents the first significant progress towards solving rigorously this problem in classical nonequilibrium statistical physics, since the groundbreaking work of Gallavotti (Phys Rev 185:308–322, 1969, Nota Interna Univ di Roma 358, 1970, Statistical mechanics. A short treatise. Theoretical and mathematical physics series, Springer, Berlin, 1999), Spohn (Commun Math Phys 60:277–290, 1978, Rev Mod Phys 52:569–611, 1980) and Boldrighini–Bunimovich–Sinai (J Stat Phys 32:477–501, 1983). The novelty is that the diffusive scaling of particle trajectory and the kinetic (Boltzmann-Grad) limit are taken simultaneously. The main ingredients are a coupling of the mechanical trajectory with the Markovian random flight process, and probabilistic and geometric controls on the efficiency of this coupling. Similar results have been earlier obtained for the weak coupling limit of classical and quantum random Lorentz gas, by Komorowski–Ryzhik (Commun Math Phys 263:277–323, 2006), respectively, Erdős–Salmhofer–Yau (Acta Math 200:211–277, 2008, Commun Math Phys 271:1–53, 2007). However, the following are substantial differences between our work and these ones: (1) The physical setting is different: low density rather than weak coupling. (2) The method of approach is different: probabilistic coupling rather than analytic/perturbative. (3) Due to (2), the time scale of validity of our diffusive approximation—expressed in terms of the kinetic time scale—is much longer and fully explicit.
49
BOGEY, C., and C. BAILLY. "Turbulence and energy budget in a self-preserving round jet: direct evaluation using large eddy simulation." Journal of Fluid Mechanics 627 (May 25, 2009): 129–60. http://dx.doi.org/10.1017/s0022112009005801.
Анотація:
An axisymmetric jet at a diameter-based Reynolds number of 1.1 × 104 is computed by a large eddy simulation (LES) in order to investigate its self-similarity region. The LES combines low-dissipation numerical schemes and explicit filtering of the flow variables to relax energy through the smaller scales discretized. The computational domain extends up to 150 jet radii in the downstream direction, which is found to be large enough to discretize a part of this region. Turbulence in the self-preserving jet is characterized by evaluating explicitly from the LES fields the second- and third-order moments of velocity, the pressure–velocity correlations as well as the budgets for the turbulent kinetic energy and for its components. Reference solutions are thus obtained. They agree well with the experimental data given by Panchapakesan & Lumley (J. Fluid Mech., vol. 246, 1963, p. 197) for a jet at the same Reynolds number. The distance required to achieve self-similarity in the LES, around 120 radii from the inflow, is particularly similar to that in the experiment. The discrepancies observed with respect to the data provided by Panchapakesan & Lumley and by Hussein, Capp & George (J. Fluid Mech., vol. 258, 1994, p. 31) for a jet at a higher Reynolds number, specially regarding the turbulence diffusion and the dissipation, are discussed. They appear largely resulting from the approximations made in the experiments to estimate the quantities that cannot be measured with accuracy. The role of the pressure terms in the energy redistribution is also clarified by the LES. Moreover, the turbulent energy budget is calculated in the jet from an equation derived from the filtered compressible Navier–Stokes equations, which includes the dissipation due to the explicit filtering. This has allowed us to assess the behaviour of the LES approach based on relaxation filtering (LES-RF) from the contributions of filtering and viscosity to energy dissipation. The filtering activity is particularly shown to adjust by itself to the grid and flow properties.
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Lenz, Stephan, Martin Geier, and Manfred Krafczyk. "Simulation of Fire with a Gas Kinetic Scheme on Distributed GPGPU Architectures." Computation 8, no. 2 (May 26, 2020): 50. http://dx.doi.org/10.3390/computation8020050.
Анотація:
The simulation of fire is a challenging task due to its occurrence on multiple space-time scales and the non-linear interaction of multiple physical processes. Current state-of-the-art software such as the Fire Dynamics Simulator (FDS) implements most of the required physics, yet a significant drawback of this implementation is its limited scalability on modern massively parallel hardware. The current paper presents a massively parallel implementation of a Gas Kinetic Scheme (GKS) on General Purpose Graphics Processing Units (GPGPUs) as a potential alternative modeling and simulation approach. The implementation is validated for turbulent natural convection against experimental data. Subsequently, it is validated for two simulations of fire plumes, including a small-scale table top setup and a fire on the scale of a few meters. We show that the present GKS achieves comparable accuracy to the results obtained by FDS. Yet, due to the parallel efficiency on dedicated hardware, our GKS implementation delivers a reduction of wall-clock times of more than an order of magnitude. This paper demonstrates the potential of explicit local schemes in massively parallel environments for the simulation of fire.