On the approximation of the Boltzmann equation in various regime - Francis Filbet

Abstract

I will present several numerical results performed with a fully deterministic scheme to discretize the Boltzmann equation of rarefied gas dynamics in a bounded domain for multi-scale problems. Periodic, specular reflection and diffusive boundary conditions will be discussed and investigated numerically. The collision operator is treated by a Fourier approximation of the collision integral, which guarantees spectral accuracy in velocity with a computational cost of M N log(N), where N is the number of degree of freedom in velocity space and M represents the the number of discrete angles of the collision kernel. This algorithm is coupled with a second order finite volume scheme in space and a time discretization allow ing to deal for rarefied regimes as well as their hydrodynamic limit. Numerical results show that the proposed approach significantly improves the near-wall non stationary flow accuracy of standard numerical methods over a wide range of Knudsen numbers. In particular when the solution to the Boltzmann equation is closed tothe local equilibrium and for slow motion flows.