Numerical Schemes of Diffusion Asymptotics and Moment Closures for Kinetic Equations

José Antonio Carrillo (1) , Thierry Goudon (2, 3) , Pauline Lafitte (2, 3) , Francesco Vecil (1)

1 UAB - Departament de Matemàtiques [Barcelona]
2 SIMPAF - SImulations and Modeling for PArticles and Fluids
3 LPP - Laboratoire Paul Painlevé - UMR 8524

We investigate different models that are intended to describe the small mean free path regime of a kinetic equation, a particular attention being paid to the moment closure by entropy minimization. We introduce a specific asymptotic-induced numerical strategy which is able to treat the stiff terms of the asymptotic diffusive regime. We evaluate on numerics the performances of the method and the abilities of the reduced models to capture the main features of the full kinetic equation.

Mots clés: Diffusion asymptotics; Moment closure; Hyperbolic systems; Asymptotic preserving schemes

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

José Antonio Carrillo, Thierry Goudon, Pauline Lafitte, Francesco Vecil. Numerical Schemes of Diffusion Asymptotics and Moment Closures for Kinetic Equations. Journal of Scientific Computing, 2008, 35, pp.113-149. ⟨10.1007/s10915-007-9181-5⟩. ⟨hal-00768401⟩