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Journal articles on the topic 'Explicit diffusive kinetic scheme'

Author: Grafiati

Published: 7 July 2024

Last updated: 31 July 2025

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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 (2003): 63–94. http://dx.doi.org/10.1090/s0025-5718-03-01549-7.

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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 (2014): 1291–319. http://dx.doi.org/10.4208/cicp.090513.151113a.

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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

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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.

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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 numeric

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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.

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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

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Lv, Maoyin, and Hao Wu. "On the nonlocal Cahn–Hilliard equation with nonlocal dynamic boundary condition and singular potential: well-posedness, regularity and asymptotic limits." Nonlinearity 38, no. 4 (2025): 045017. https://doi.org/10.1088/1361-6544/adbcf2.

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Abstract We consider a class of nonlocal Cahn–Hilliard equations in a bounded domain Ω ⊂ R d ( d ∈ { 2 , 3 } ) , subject to a nonlocal kinetic rate dependent dynamic boundary condition. This diffuse interface model describes phase separation processes with possible long-range interactions both within the bulk material and on its boundary. The kinetic rate 1 / L , with L ∈ [ 0 , + ∞ ] , distinguishes different types of bulk-boundary interactions. For the initial boundary value problem endowed with general singular potentials, including the physically relevant logarithmic potential, we first est

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Eckermann, Stephen D. "Explicitly Stochastic Parameterization of Nonorographic Gravity Wave Drag." Journal of the Atmospheric Sciences 68, no. 8 (2011): 1749–65. http://dx.doi.org/10.1175/2011jas3684.1.

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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

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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.

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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 mech

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8

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 (2020): 4247–65. http://dx.doi.org/10.1175/mwr-d-20-0102.1.

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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 turbul

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9

Deng, Aijun, and David R. Stauffer. "On Improving 4-km Mesoscale Model Simulations." Journal of Applied Meteorology and Climatology 45, no. 3 (2006): 361–81. http://dx.doi.org/10.1175/jam2341.1.

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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

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10

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.

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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,

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11

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 (2024): 2525–45. http://dx.doi.org/10.5194/gmd-17-2525-2024.

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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

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12

Artichowicz, Wojciech, and Dariusz Gąsiorowski. "Computationally Efficient Solution of a 2D Diffusive Wave Equation Used for Flood Inundation Problems." Water 11, no. 10 (2019): 2195. http://dx.doi.org/10.3390/w11102195.

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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

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13

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 (2024): 217. http://dx.doi.org/10.3390/axioms13040217.

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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 consi

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14

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 (2018): 275–96. http://dx.doi.org/10.1515/cmam-2017-0021.

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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

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15

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 (2019): 276–87. http://dx.doi.org/10.2166/aqua.2019.091.

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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 thos

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16

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 (2013): A22—A51. http://dx.doi.org/10.1137/110842855.

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17

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 (1997): 193–204. http://dx.doi.org/10.1006/jcph.1997.5673.

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18

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.

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<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 demo

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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.20231568.

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<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 demo

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20

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.

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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

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21

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 (2013): 336–61. http://dx.doi.org/10.1137/110851687.

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22

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 (2021): 10199–213. http://dx.doi.org/10.5194/acp-21-10199-2021.

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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 c

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23

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.

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<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 stu

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24

Wang, Dean, and Zuolong Zhu. "A Revisit to CMFD Schemes: Fourier Analysis and Enhancement." Energies 14, no. 2 (2021): 424. http://dx.doi.org/10.3390/en14020424.

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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

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25

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 (2017): 889–912. http://dx.doi.org/10.4208/cicp.oa-2016-0261.

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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

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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 (2005): 106. http://dx.doi.org/10.5380/reterm.v4i2.5406.

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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 s

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27

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 (2021): 2949–80. http://dx.doi.org/10.1051/m2an/2021077.

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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 som

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28

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.

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<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 su

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29

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.

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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 reprod

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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 (2013): 1233–41. http://dx.doi.org/10.1175/jas-d-12-0216.1.

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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

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31

SUZUKI, KOSUKE, and TAKAJI INAMURO. "AN IMPROVED LATTICE KINETIC SCHEME FOR INCOMPRESSIBLE VISCOUS FLUID FLOWS." International Journal of Modern Physics C 25, no. 01 (2013): 1340017. http://dx.doi.org/10.1142/s0129183113400172.

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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 schem

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32

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.

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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 (2021): 869–99. http://dx.doi.org/10.1007/s00211-021-01184-w.

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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 nonconform

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Nagy, Endre, and Imre Hegedüs. "Diffusive Plus Convective Mass Transport, Accompanied by Biochemical Reaction, Across Capillary Membrane." Catalysts 10, no. 10 (2020): 1115. http://dx.doi.org/10.3390/catal10101115.

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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 v

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35

Chijonkov, E. V. "ON THE NUMERICAL SOLUTION OF THE VLASOV-AMPERE EQUATIONS." Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki 64, no. 7 (2024): 1268–80. https://doi.org/10.31857/s0044466924070116.

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An implicit McCormack-type scheme is constructed for the kinetic plasma model based on the VlasovAmpere equations. Compared to the explicit scheme, it has a weaker stability constraint, but retains the same computational efficiency, i.e. it does not use internal iterations. In this case, the error of the total energy corresponds to the second order of accuracy of the algorithm, and the total charge (number of particles) is stored at the grid level. The formation of plasma waves excited by a short powerful laser pulse is considered as a simulated physical process.

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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 (2019): 216–23. http://dx.doi.org/10.15446/dyna.v86n210.78596.

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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 dist

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37

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 (2021): 113206. http://dx.doi.org/10.1088/1742-5468/ac382d.

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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 t

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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.

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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.

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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 (2000): 1121–49. http://dx.doi.org/10.1142/s0218202500000562.

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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 s

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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 (2019): 336–41. http://dx.doi.org/10.14429/dsj.69.13536.

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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 analysi

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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 (2019): 1184–205. http://dx.doi.org/10.1002/num.22345.

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ZHANG Chuang and GUO Zhaoli. "Discrete unified gas kinetic scheme and its application in multi-scale heat conduction." Acta Physica Sinica 74, no. 17 (2025): 0. https://doi.org/10.7498/aps.74.20250694.

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Multiscale particle transport problems are widely present in the fields of precision manufacturing, nanomaterials, energy and power, national defense and military. Such problems involve large-scale length and time scales, which pose great challenges to physical modeling and numerical simulations. To study multiscale particle transport problems, cross-scale numerical simulation based on the Boltzmann transport equation has become an effective method, but the nonlinear, multi-scale, and high-dimensional characteristics of the equation pose great challenges to the stability, compatibility, comput

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Lutsko, Christopher, and Bálint Tóth. "Invariance Principle for the Random Lorentz Gas—Beyond the Boltzmann-Grad Limit." Communications in Mathematical Physics 379, no. 2 (2020): 589–632. http://dx.doi.org/10.1007/s00220-020-03852-8.

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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

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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 (2011): 25–36. http://dx.doi.org/10.3329/jname.v8i1.7250.

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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

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Vick, Brian. "Multi-physics Modeling Using Cellular Automata." Complex Systems 17, no. 1 (2007): 65–78. http://dx.doi.org/10.25088/complexsystems.17.1.65.

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This paper proposes a new modeling and solution method that is relatively simple yet powerful enough to handle complex multi-physics problems. The new methodology is based on a combination of cellular automata, finite difference, and analytical analysis concepts. The basic idea is to construct a cascading sequence of simple, explicit rules of evolution, rather than attempt to solve complicated partial differential equations. The resulting scheme is computationally explicit yet numerically stable. In addition to significant modeling flexibility, the cellular automata environment lends itself to

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Wyss, Alejandra, and Arturo Hidalgo. "Modeling COVID-19 Using a Modified SVIR Compartmental Model and LSTM-Estimated Parameters." Mathematics 11, no. 6 (2023): 1436. http://dx.doi.org/10.3390/math11061436.

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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 validate

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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.

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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 f

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Manivannan, Vinoth, Mandar M. Inamdar, and Ranjith Padinhateeri. "Role of diffusion and reaction of the constituents in spreading of histone modification marks." PLOS Computational Biology 20, no. 7 (2024): e1012235. http://dx.doi.org/10.1371/journal.pcbi.1012235.

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Cells switch genes ON or OFF by altering the state of chromatin via histone modifications at specific regulatory locations along the chromatin polymer. These gene regulation processes are carried out by a network of reactions in which the histone marks spread to neighboring regions with the help of enzymes. In the literature, this spreading has been studied as a purely kinetic, non-diffusive process considering the interactions between neighboring nucleosomes. In this work, we go beyond this framework and study the spreading of modifications using a reaction-diffusion (RD) model accounting for

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Herbin, Raphaèle, Jean-Claude Latché, and Trung Tan Nguyen. "Consistent segregated staggered schemes with explicit steps for the isentropic and full Euler equations." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 3 (2018): 893–944. http://dx.doi.org/10.1051/m2an/2017055.

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In this paper, we build and analyze the stability and consistency of decoupled schemes, involving only explicit steps, for the isentropic Euler equations and for the full Euler equations. These schemes are based on staggered space discretizations, with an upwinding performed with respect to the material velocity only. The pressure gradient is defined as the transpose of the natural velocity divergence, and is thus centered. The velocity convection term is built in such a way that the solutions satisfy a discrete kinetic energy balance, with a remainder term at the left-hand side which is shown

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