A conservative semi-Lagrangian method for inhomogeneous Boltzmann equation

The Boltzmann equation is well-known for its good predictability of behaviors of rarefied gas flows, which may not be resolved enough by continuum models. In this work, we propose a high order conservative semi-Lagrangian method for the inhomogeneous Boltzmann equation of rarefied gas dynamics. We adopt a semi-Lagrangian scheme for the convection term, which enables us to avoid CFL-type restrictions on the time step. Also, we use a fast spectral method for computation of the collision operator. In order to preserve conservative quantities, we combine a high order conservative reconstruction and a weighted optimization technique. Several numerical tests illustrate the accuracy and efficiency of the proposed method.