Thomas Rey
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View article: Discrete $H$-theorem for a finite volume discretization of a nonlinear kinetic system: application to hypocoercivity
Discrete $H$-theorem for a finite volume discretization of a nonlinear kinetic system: application to hypocoercivity Open
In this article, we study the long-time behavior of a finite-volume discretization for a nonlinear kinetic reaction model involving two interacting species. Building upon the seminal work of [Favre, Pirner, Schmeiser, ARMA, 2023], we exten…
View article: The Boltzmann Equation for a Multi-Species Inelastic Mixture
The Boltzmann Equation for a Multi-Species Inelastic Mixture Open
View article: Formal derivation of an isentropic two-phase flow model from the multi-species Boltzmann equation
Formal derivation of an isentropic two-phase flow model from the multi-species Boltzmann equation Open
Starting from the multi-species Boltzmann equation for a gas mixture, we propose the formal derivation of the isentropic two-phase flow model introduced in [Romenski, E., and Toro, E. F., Comput. Fluid Dyn. J., 13 (2004)]. We examine the a…
View article: Hierarchical dynamic domain decomposition for the multiscale Boltzmann equation
Hierarchical dynamic domain decomposition for the multiscale Boltzmann equation Open
In this work, we present a hierarchical domain decomposition method for the multi-scale Boltzmann equation based on moment realizability matrices, a concept introduced by Levermore, Morokoff, and Nadiga in \cite{lev-mor-nad-1998}. This cri…
View article: A Parareal in time numerical method for the collisional Vlasov equation in the hyperbolic scaling
A Parareal in time numerical method for the collisional Vlasov equation in the hyperbolic scaling Open
We present the design of a multiscale parareal method for kinetic equations in the fluid dynamic regime. The goal is to reduce the cost of a fully kinetic simulation using a parallel in time procedure. Using the multiscale property of kine…
View article: Hierarchical Dynamic Domain Decomposition for the Multiscale Boltzmann Equation
Hierarchical Dynamic Domain Decomposition for the Multiscale Boltzmann Equation Open
View article: The Boltzmann equation for a multi-species inelastic mixture
The Boltzmann equation for a multi-species inelastic mixture Open
A granular gas is a collection of macroscopic particles that interact through energy-dissipating collisions, also known as inelastic collisions. This inelasticity is characterized by a collision mechanics in which mass and momentum are con…
View article: Discrete hypocoercivity for a nonlinear kinetic reaction model
Discrete hypocoercivity for a nonlinear kinetic reaction model Open
In this article we propose a finite-volume discretization of a one-dimensional nonlinear reaction kinetic model proposed in Neumann & Schmeiser (2016), which describes a two-species recombination-generation process. Specifically, we establ…
View article: On deterministic numerical methods for the quantum Boltzmann-Nordheim equation. I. Spectrally accurate approximations, Bose-Einstein condensation, Fermi-Dirac saturation
On deterministic numerical methods for the quantum Boltzmann-Nordheim equation. I. Spectrally accurate approximations, Bose-Einstein condensation, Fermi-Dirac saturation Open
View article: Hybrid Kinetic/Fluid numerical method for the Vlasov-Poisson-BGK equation in the diffusive scaling
Hybrid Kinetic/Fluid numerical method for the Vlasov-Poisson-BGK equation in the diffusive scaling Open
This short note presents an extension of the hybrid, model-adaptation method introduced in [T.~Laidin, \textit{arXiv 2202.03696}, 2022] for linear collisional kinetic equations in a diffusive scaling to the nonlinear mean-field Vlasov-Pois…
View article: Contributions à l'analyse mathématique et numérique d'équations cinétiques multi-échelles
Contributions à l'analyse mathématique et numérique d'équations cinétiques multi-échelles Open
Cette habilitation couvre une grande partie des recherches que j'ai effectué depuis mon doctorat. Les principales questions que je me suis posées concernent le champ de la modélisation, de l'analyse et des simulations numériques de système…
View article: Hybrid Kinetic/Fluid Numerical Method for the Vlasov-Poisson-BGK Equation in the Diffusive Scaling
Hybrid Kinetic/Fluid Numerical Method for the Vlasov-Poisson-BGK Equation in the Diffusive Scaling Open
View article: Moment Preserving Fourier–Galerkin Spectral Methods and Application to the Boltzmann Equation
Moment Preserving Fourier–Galerkin Spectral Methods and Application to the Boltzmann Equation Open
Spectral methods, thanks to the high accuracy and the possibility of using fast algorithms, represent an effective way to approximate collisional kinetic equations in kinetic theory. On the other hand, the loss of some local invariants can…
View article: Projective and telescopic projective integration for non-linear kinetic mixtures
Projective and telescopic projective integration for non-linear kinetic mixtures Open
View article: Continuous limits of large plant-pollinator random networks and some applications
Continuous limits of large plant-pollinator random networks and some applications Open
We study a stochastic individual-based model of interacting plant and pollinator species through a bipartite graph: each species is a node of the graph, an edge representing interactions between a pair of species. The dynamics of the syste…
View article: KINEBEC - Numerical simulation of Boltzmann-Nordheim equation
KINEBEC - Numerical simulation of Boltzmann-Nordheim equation Open
KINEBEC is a simulation code developed in C dedicated to classical and quantum Boltzmann equations in 2D and 3D in velocity.This code is based on spectral methods in velocity and can uses MPI, OpenMP or CUDA tools for speeding up its execu…
View article: Projective and Telescopic Projective Integration for Non-Linear Kinetic Mixtures
Projective and Telescopic Projective Integration for Non-Linear Kinetic Mixtures Open
We propose fully explicit projective integration and telescopic projective integration schemes for the multispecies Boltzmann and Bhatnagar-Gross-Krook (BGK) equations. The methods employ a sequence of small forward-Euler steps, intercalat…
View article: Moment preserving Fourier-Galerkin spectral methods and application to the Boltzmann equation
Moment preserving Fourier-Galerkin spectral methods and application to the Boltzmann equation Open
Spectral methods, thanks to the high accuracy and the possibility of using fast algorithms, represent an effective way to approximate collisional kinetic equations in kinetic theory. On the other hand, the loss of some local invariants can…
View article: Moment preserving Fourier-Galerkin spectral methods and application to\n the Boltzmann equation
Moment preserving Fourier-Galerkin spectral methods and application to\n the Boltzmann equation Open
Spectral methods, thanks to the high accuracy and the possibility of using\nfast algorithms, represent an effective way to approximate collisional kinetic\nequations in kinetic theory. On the other hand, the loss of some local\ninvariants …
View article: On the stability of equilibrium preserving spectral methods for the homogeneous Boltzmann equation
On the stability of equilibrium preserving spectral methods for the homogeneous Boltzmann equation Open
View article: Recent development in kinetic theory of granular materials:analysis and numerical methods
Recent development in kinetic theory of granular materials:analysis and numerical methods Open
View article: On Deterministic Numerical Methods for the Quantum Boltzmann-Nordheim Equation. I. Spectrally Accurate Approximations, Bose-Einstein Condensation, Fermi-Dirac Saturation
On Deterministic Numerical Methods for the Quantum Boltzmann-Nordheim Equation. I. Spectrally Accurate Approximations, Bose-Einstein Condensation, Fermi-Dirac Saturation Open
View article: Recent Development in Kinetic Theory of Granular Materials: Analysis and Numerical Methods
Recent Development in Kinetic Theory of Granular Materials: Analysis and Numerical Methods Open
View article: Convergence of knowledge in a stochastic cultural evolution model with population structure, social learning and credibility biases
Convergence of knowledge in a stochastic cultural evolution model with population structure, social learning and credibility biases Open
Understanding how knowledge emerges and propagates within groups is crucial to explain the evolution of human populations. In this work, we introduce a mathematically oriented model that draws on individual-based approaches, inhomogeneous …
View article: On the stability of equilibrium preserving spectral methods for the\n homogeneous Boltzmann equation
On the stability of equilibrium preserving spectral methods for the\n homogeneous Boltzmann equation Open
Spectral methods, thanks to the high accuracy and the possibility to use fast\nalgorithms, represent an effective way to approximate the Boltzmann collision\noperator. On the other hand, the loss of some local invariants leads to the\nwron…
View article: On the stability of equilibrium preserving spectral methods for the homogeneous Boltzmann equation
On the stability of equilibrium preserving spectral methods for the homogeneous Boltzmann equation Open
Spectral methods, thanks to the high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the Boltzmann collision operator. On the other hand, the loss of some local invariants leads to the wrong l…
View article: Recent development in kinetic theory of granular materials: analysis and numerical methods
Recent development in kinetic theory of granular materials: analysis and numerical methods Open
Over the past decades, kinetic description of granular materials has received a lot of attention in mathematical community and applied fields such as physics and engineering. This article aims to review recent mathematical results in kinet…
View article: Finite Volume Method for a System of Continuity Equations Driven by Nonlocal Interactions
Finite Volume Method for a System of Continuity Equations Driven by Nonlocal Interactions Open
View article: Finite Volume Method for a System of Continuity Equations Driven by\n Nonlocal Interactions
Finite Volume Method for a System of Continuity Equations Driven by\n Nonlocal Interactions Open
We present a new finite volume method for computing numerical approximations\nof a system of nonlocal transport equation modeling interacting species. This\nmethod is based on the work [F. Delarue, F. Lagoutire, N. Vauchelet,\nConvergence …
View article: Convergence of knowledge in a cultural evolution model with population structure, random social learning and credibility biases
Convergence of knowledge in a cultural evolution model with population structure, random social learning and credibility biases Open
Understanding how knowledge is created and propagates within groups is crucial to explain how human populations have evolved through time. Anthropologists have relied on different theoretical models to address this question. In this work, …