A new asymptotic preserving scheme based on micro-macro formulation for linear kinetic equations in the diffusion limit
Language
en
Article de revue
This item was published in
SIAM Journal on Scientific Computing. 2008, vol. 31, n° 1, p. 334-368
Society for Industrial and Applied Mathematics
English Abstract
We propose a new numerical scheme for linear transport equations. It is based on a decomposition of the distribution function into equilibrium and nonequilibrium parts. We also use a projection technique that allows us to ...Read more >
We propose a new numerical scheme for linear transport equations. It is based on a decomposition of the distribution function into equilibrium and nonequilibrium parts. We also use a projection technique that allows us to reformulate the kinetic equation into a coupled system of an evolution equation for the macroscopic density and a kinetic equation for the nonequilibrium part. By using a suitable time semi-implicit discretization, our scheme is able to accurately approximate the solution in both kinetic and diffusion regimes. It is asymptotic preserving in the following sense: when the mean free path of the particles is small, our scheme is asymptotically equivalent to a standard numerical scheme for the limit diffusion model. A uniform stability property is proved for the simple telegraph model. Various boundary conditions are studied. Our method is validated in one-dimensional cases by several numerical tests and comparisons with previous asymptotic preserving schemes.Read less <
English Keywords
transport equations
diffusion limit
asymptotic preserving schemes
stiff terms
Origin
Hal imported