Microscopically implicit-macroscopically explicit schemes for the BGK equation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:231

Article

Pieraccini, Sandra¹  Puppo, Gabriella¹ 

[1] Politecn Torino, Dipartimento Matemat, I-10129 Turin, Italy

关键词: BGK model;    Kinetic equations;    Implicit schemes;    Hybrid methods;   

DOI  :  10.1016/j.jcp.2011.08.027

来源: Elsevier

【 摘 要 】

In this work a new class of numerical methods for the BGK model of kinetic equations is introduced. The schemes proposed are implicit with respect to the distribution function, while the macroscopic moments are evolved explicitly. In this fashion, the stability condition on the time step coincides with a macroscopic CFL, evaluated using estimated values for the macroscopic velocity and sound speed. Thus the stability restriction does not depend on the relaxation time and it does not depend on the microscopic velocity of energetic particles either. With the technique proposed here, the updating of the distribution function requires the solution of a linear system of equations, even though the BGK model is highly non linear. Thus the proposed schemes are particularly effective for high or moderate Mach numbers, where the macroscopic CFL condition is comparable to accuracy requirements. We show results for schemes of order 1 and 2, and the generalization to higher order is sketched. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free