A hierarchy of hybrid numerical methods for multi-scale kinetic equations

Francis Filbet (1, 2) , Thomas Rey (3, 4)

1 MMCS - Modélisation mathématique, calcul scientifique
2 KALiFFE - Kinetic models AppLIed for Future of Fusion Energy
3 RAPSODI - Reliable numerical approximations of dissipative systems
4 CSCAMM - Center for Scientific Computation and Mathematical Modeling

In this paper, we construct a hierarchy of hybrid numerical methods for multi-scale kinetic equations based on moment realizability matrices, a concept introduced by Levermore, Mo- rokoff and Nadiga. Following such a criterion, one can consider hybrid scheme where the hydrodynamic part is given either by the compressible Euler or Navier-Stokes equations, or even with more general models, such as the Burnett or super-Burnett systems.

Domaines: Analyse numérique [math.NA]

Francis Filbet, Thomas Rey. A hierarchy of hybrid numerical methods for multi-scale kinetic equations. SIAM Journal on Scientific Computing, 2015, 37 (3), pp.A1218-A1247. ⟨10.1137/140958773⟩. ⟨hal-00951980⟩