Journal article
A bi-fidelity method for the multiscale Boltzmann equation with random parameters
Journal of computational physics, Vol.402(C), p.108914
02/01/2020
DOI: 10.1016/j.jcp.2019.108914
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.
Details
- Title: Subtitle
- A bi-fidelity method for the multiscale Boltzmann equation with random parameters
- Creators
- Liu Liu - The University of Texas at AustinXueyu Zhu - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Journal of computational physics, Vol.402(C), p.108914
- DOI
- 10.1016/j.jcp.2019.108914
- ISSN
- 0021-9991
- eISSN
- 1090-2716
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Number of pages
- 23
- Grant note
- DE-SC0016283 / DOE-Simulation Center for Runaway Electron Avoidance and Mitigation 504054 / Simons Foundation
- Language
- English
- Date published
- 02/01/2020
- Academic Unit
- Mathematics
- Record Identifier
- 9984240774202771
Metrics
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