Locally refined discrete velocity grids for stationary rarefied flow simulations

Céline Baranger (1) , Jean Claudel (1) , Nicolas Hérouard (2) , Luc Mieussens (2)

1 CESTA - Centre d'études scientifiques et techniques d'Aquitaine
2 IMB - Institut de Mathématiques de Bordeaux

Most of deterministic solvers for rarefied gas dynamics use discrete velocity (or discrete ordinate) approximations of the distribution function on a Cartesian grid. This grid must be sufficiently large and fine to describe the distribution functions at every space position in the computational domain. For 3-dimensional hypersonic flows, like in re-entry problems, this induces much too dense velocity grids that cannot be practically used, for memory storage requirements. In this article, we present an approach to generate automatically a locally refined velocity grid adapted to a given simulation. This grid contains much less points than a standard Cartesian grid and allows us to make realistic 3-dimensional simulations at a reduced cost, with a comparable accuracy.

Mots clés: rarefied flow simulation; hypersonic flows; re-entry problem; transition regime; BGK model; discrete velocity model

Domaines: Analyse numérique [math.NA]

Céline Baranger, Jean Claudel, Nicolas Hérouard, Luc Mieussens. Locally refined discrete velocity grids for stationary rarefied flow simulations. Journal of Computational Physics, 2014, 257 (15), pp.572-593. ⟨10.1016/j.jcp.2013.10.014⟩. ⟨hal-00815967v2⟩