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

• Published in: Solid-state electronics Vol. 198; p. 108457
• Main Authors: Cha, Suhyeong, Hong, Sung-Min
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-12-2022
• Subjects: Boltzmann transport equation; Spherical harmonics expansion; Stabilization scheme; Boltzmann transport equation; Stabilization scheme; Spherical harmonics expansion
• ISSN: 0038-1101; 1879-2405
• DOI: 10.1016/j.sse.2022.108457

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.
•A numerical stabilization method for a deterministic Boltzmann solver is proposed.•Distribution functions at past time instances are accessible without interpolation.•The proposed method can be readily applied to the transient simulation.