Fast Numerical Method for 2D Initial-Boundary Value Problems for the Boltzmann Equation

摘要

We present a new numerical scheme for the initial-boundary value problem for the Boltzmann equation in two-dimensional physical space. It is based on a splitting procedure in which the collision equation is solved using the adaptive algorithm for the computation of the full three-dimensional Boltzmann collision operator on non-uniform velocity grids introduced in the previous paper by the authors. The computation of the collision operator is performed in parallel for every physical grid cell. For the two-dimensional transport equation we use a second order finite volume method. The numerical example showing the effectiveness of our method is given.