Asymptotic-Preserving methods and multiscale models for plasma physics

Asymptotic Preserving and Multiscale Methods for Kinetic and Hyperbolic Problems

Abstract. This presentation concerns the numerical approximation of a PDE system which models cell movements according to a chemoattractant concentration. The system under consideration turns out to couple a hyperbolic system with a diffusive equation. The solutions of such a model satisfy several properties to be preserved at the numerical level. Indeed, the solutions may contain vacuum, satis...

Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations

Many kinetic models of the Boltzmann equation have a diiusive scaling that leads to the Navier-Stokes type parabolic equations as the small scaling parameter approaches zero. In practical applications, it is desirable to develop a class of numerical schemes that can work uniformly with respect to this relaxation parameter, from the rareeed kinetic regimes to the hydrodynamic diiusive regimes. A...

Asymptotic preserving boundary conditions for kinetic models

Structure and structure-preserving algorithms for plasma physics

Efficient asymptotic preserving deterministic methods for the Boltzmann equation

1 The Boltzmann equation 6 1.1 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Physical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Fluid limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 Other collis...