ON DETERMINISTIC APPROXIMATION OF THE BOLTZMANN EQUATION IN A BOUNDED DOMAIN

In this paper we present several numerical results performed with a fully deterministic scheme to discretize the Boltzmann equation of rarefied gas dynamics in a bounded domain for multiscale problems. Periodic, specular reflection and diffusive boundary conditions are 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 degrees of freedom in velocity space and M represents 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 allowing us to deal for rarefied regimes as well as their hydrodynamic limit. Our numerical results show that the proposed approach significantly improves the near-wall nonstationary flow accuracy of standard numerical methods over a wide range of Knudsen numbers, in particular when the solution to the Boltzmann equation is close to the local equilibrium and for slow motion flows.