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

Journal Article · · Journal of Computational Physics
 [1];  [2]
  1. Univ. of Texas, Austin, TX (United States). Oden Inst. for Computational Engineering and Sciences; OSTI
  2. Univ. of Iowa, Iowa City, IA (United States)
+ Show Author Affiliations
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 bi-fidelity approximation can capture well the macroscopic quantities of the solution to the Boltzmann equation in the random space. Additionally, 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.
Research Organization:
Univ. of Texas, Austin, TX (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
SC0016283
OSTI ID:
1802916
Alternate ID(s):
OSTI ID: 1775903
Journal Information:
Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 402; ISSN 0021-9991
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

97 MATHEMATICS AND COMPUTING
Bi-fidelity models
Boltzmann equation
Computer science
Multiple scales
Physics
Stochastic collocation
Uncertainty