Numerical methods for kinetic equations
In this survey we consider the development and mathematical analysis of numerical
methods for kinetic partial differential equations. Kinetic equations represent a way of …
methods for kinetic partial differential equations. Kinetic equations represent a way of …
Implicit-explicit Runge--Kutta schemes for hyperbolic systems and kinetic equations in the diffusion limit
We consider implicit-explicit (IMEX) Runge--Kutta (RK) schemes for hyperbolic systems with
stiff relaxation in the so-called diffusion limit. In such a regime the system relaxes towards a …
stiff relaxation in the so-called diffusion limit. In such a regime the system relaxes towards a …
Large time step and asymptotic preserving numerical schemes for the gas dynamics equations with source terms
We propose large time step and asymptotic preserving schemes for the gas dynamics
equations with external forces and friction terms. By asymptotic preserving, we mean that the …
equations with external forces and friction terms. By asymptotic preserving, we mean that the …
Asymptotic preserving and positive schemes for radiation hydrodynamics
In view of radiation hydrodynamics computations, we propose an implicit and positive
numerical scheme that captures the diffusion limit of the two-moments approximate model …
numerical scheme that captures the diffusion limit of the two-moments approximate model …
Asymptotic-preserving schemes for fluid models of plasmas
These notes summarize a series of works related to the numerical approximation of plasma
fluid problems. We construct so-called'Asymptotic-Preserving'schemes which are valid for a …
fluid problems. We construct so-called'Asymptotic-Preserving'schemes which are valid for a …
Asymptotic preserving HLL schemes
This work concerns the derivation of HLL schemes to approximate the solutions of systems
of conservation laws supplemented by source terms. Such a system contains many models …
of conservation laws supplemented by source terms. Such a system contains many models …
Godunov-type schemes for hyperbolic systems with parameter-dependent source: the case of Euler system with friction
Well-balanced or asymptotic preserving schemes are receiving an increasing amount of
interest. This paper gives a precise setting for studying both properties in the case of Euler …
interest. This paper gives a precise setting for studying both properties in the case of Euler …
High-order asymptotic-preserving methods for fully nonlinear relaxation problems
We study solutions to nonlinear hyperbolic systems with fully nonlinear relaxation terms in
the limit of, both, infinitely stiff relaxation and arbitrary late time. In this limit, the dynamics is …
the limit of, both, infinitely stiff relaxation and arbitrary late time. In this limit, the dynamics is …
Asymptotic-preserving Monte Carlo methods for transport equations in the diffusive limit
We develop a new Monte Carlo method that solves hyperbolic transport equations with stiff
terms, characterized by a (small) scaling parameter. In particular, we focus on systems which …
terms, characterized by a (small) scaling parameter. In particular, we focus on systems which …
A realizability-preserving discontinuous Galerkin method for the M1 model of radiative transfer
The M1 model for radiative transfer coupled to a material energy equation in planar
geometry is studied in this paper. For this model to be well-posed, its moment variables must …
geometry is studied in this paper. For this model to be well-posed, its moment variables must …