Convergence of a semi-Lagrangian scheme for the ellipsoidal BGK model of the bol tzmann equation

The ellipsoidal Bhatnagar-Gross-Krook (BGK) model is a generalized version of the original BGK model designed to reproduce the physical Prandtl number in the Navier-Stokes limit. In this paper, we propose a new implicit semi-Lagrangian scheme for the ellipsoidal BGK model, which, by exploiting special structures of the ellipsoidal Gaussian, can be transformed into a semiexplicit form, guaranteeing the stability of the implicit methods and the efficiency of the explicit methods at the same time. We then derive an error estimate of this scheme in a weighted L ^∞ norm. Our convergence estimate holds uniformly in the whole range of relaxation parameter ν including ν = 0, which corresponds to the original BGK model.