A positive preserving gas‐kinetic scheme for relativistic Vlasov‐Bhatnagar‐Gross‐Krook‐Maxwell model

Abstract

A positive preserving scheme is proposed for Vlasov-Bhatnagar-Gross-Krook (BGK)-Maxwell model to simulate the laser-plasma-interaction with relativistic effect. The Strang-splitting method is adopted and the Vlasov-BGK equation is divided into two parts, the kinetic part and acceleration part. Asymptotic gas-kinetic scheme is designed for the kinetic part and the solver for p direction is analytically accurate along the characteristic. Maxwell equations are solved by characteristic line method. The scheme is proved positive preserving. Stimulated Raman Scattering and Relativistic Modulational Instability are used to verify the validity of scheme.

Positivity‐preserving scheme for the flux reconstruction framework with a novel implementation

“…Remarkable works such as References 5‐7 report great improvement of robustness owing to its application. The positivity‐preserving property may be realized through a posteriori correction or reconstruction, 8 and extended to more problems 9‐12 . In References 13‐15, a popular positivity‐preserving scheme is developed for solving different equations on various types of meshes.…”

“…The positivity-preserving property may be realized through a posteriori correction or reconstruction, 8 and extended to more problems. [9][10][11][12] In References 13-15, a popular positivity-preserving scheme is developed for solving different equations on various types of meshes. In this scheme, a positivity-preserving flux in the local Lax-Friedrichs form is adopted.…”