Approximate H-transformation for numerical stabilization of a deterministic Boltzmann transport equation solver based on a spherical harmonics expansion

Abstract

In this work, we propose a numerical stabilization method for a deterministic Boltzmann transport equation solver based on a spherical harmonics expansion. In the proposed scheme, the approximate H-transformation, a new energy variable approximately follows the total energy. An additional term is generated out of the free-streaming operator and it should be implemented properly. When the kinetic energy is fixed, the distribution function at that energy can be directly accessible at any time instance. The proposed scheme is implemented in our in-house deterministic Boltzmann transport equation solver. The numerical simulation results demonstrate that the proposed stabilization scheme works properly without any numerical difficulties.