Numerical solution of the Boltzmann Equation using fully conservative difference scheme based on the Fast Fourier Transform

Abstract

An effective deterministic method based on the Fast Fourier Transform (FFT) for the Boltzmann equation with Maxwell molecules is considered. The global existence, uniqueness and boundness of the discrete solution is proved. The analytical form of the first 13 moments of the solution is derived. An effective procedure for the conservation of the macroscopic quantities is described. The results of some numerical tests are presented.