A bi-fidelity method for the multiscale Boltzmann equation with random parameters

JOURNAL OF COMPUTATIONAL PHYSICS

卷:402

Article

Liu, Liu¹  Zhu, Xueyu² 

[1] Univ Texas Austin, Oden Inst Computat Engn & Sci, Austin, TX 78712 USA

[2] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

关键词: Boltzmann equation;    Uncertainty;    Bi-fidelity models;    Multiple scales;    Stochastic collocation;   

DOI  :  10.1016/j.jcp.2019.108914

来源: Elsevier

【 摘 要 】

In this paper, we study the multiscale Boltzmann equation with multi-dimensional random parameters by a bi-fidelity stochastic collocation (SC) method developed in [52,70,71]. By choosing the compressible Euler system as the low-fidelity model, we adapt the bi-fidelity SC method to combine computational efficiency of the low-fidelity model with high accuracy of the high-fidelity (Boltzmann) model. With only a small number of high-fidelity asymptotic-preserving solver runs for the Boltzmann equation, the bifidelity approximation can capture well the macroscopic quantities of the solution to the Boltzmann equation in the random space. A priori estimate on the accuracy between the high- and bi-fidelity solutions together with a convergence analysis is established. Finally, we present extensive numerical experiments to verify the efficiency and accuracy of our proposed method. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free