Local discrete velocity grids for deterministic rarefied flow simulations

Stéphane Brull (1) , Luc Mieussens (1)

1 IMB - Institut de Mathématiques de Bordeaux

Most of numerical methods for deterministic simulations of rarefied gas flows use the discrete velocity (or discrete ordinate) approximation. In this approach, the kinetic equation is approximated with a global velocity grid. The grid must be large and fine enough to capture all the distribution functions, which is very expensive for high speed flows (like in hypersonic aerodynamics). In this article, we propose to use instead different velocity grids that are local in time and space: these grids dynamically adapt to the width of the distribution functions. The advantages and drawbacks of the method are illustrated in several 1D test cases.

Mots clés: kinetic equations; discrete velocity model; deterministic method; rarefied gas dynamics

Domaines: Analyse numérique [math.NA]

Stéphane Brull, Luc Mieussens. Local discrete velocity grids for deterministic rarefied flow simulations. Journal of Computational Physics, 2014, 266 (1), pp.22-46. ⟨10.1016/j.jcp.2014.01.050⟩. ⟨hal-00808613v3⟩