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A bi-fidelity method for the multiscale Boltzmann equation with random parameters
Journal article   Peer reviewed

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

Liu Liu and Xueyu Zhu
Journal of computational physics, Vol.402(C), p.108914
02/01/2020
DOI: 10.1016/j.jcp.2019.108914
url
https://arxiv.org/pdf/1905.09023View
Open Access

Abstract

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.
Computer Science Computer Science, Interdisciplinary Applications Physical Sciences Physics Physics, Mathematical Science & Technology Technology

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