On stochastic Galerkin approximation of the nonlinear Boltzmann equation with uncertainty in the fluid regime

JOURNAL OF COMPUTATIONAL PHYSICS

卷:397

Article

Hu, Jingwei¹  Jin, Shi²  Shu, Ruiwen³ 

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] Shanghai Jiao Tong Univ, MOE LSC, Inst Nat Sci, Sch Math Sci, Shanghai 200240, Peoples R China

[3] Univ Maryland, Dept Math, College Pk, MD 20742 USA

关键词: Boltzmann equation with uncertainty;    Stochastic Galerkin;    Asymptotic-preserving schemes;    Fluid dynamic limit;   

DOI  :  10.1016/j.jcp.2019.07.037

来源: Elsevier

【 摘 要 】

The Boltzmann equation may contain uncertainties in initial/boundary data or collision kernel. To study the impact of these uncertainties, a stochastic Galerkin (sG) method was proposed in [18] and studied in the kinetic regime. When the system is close to the fluid regime (the Knudsen number is small), the method would become prohibitively expensive due to the stiff collision term. In this work, we develop efficient sG methods for the Boltzmann equation that work for a wide range of Knudsen numbers, and investigate, in particular, their behavior in the fluid regime. (C) 2019 Published by Elsevier Inc.

【 授权许可】

Free