A bi-fidelity method for the Boltzmann equation with random parameters and multiple scales
Time: 2019-08-14
Published By: Ying Hao
Speaker(s): Liu Liu (The University of Texas at Austin)
Time: 16:00-17:00 August 21, 2019
Venue: Room 9, Quan Zhai, BICMR
Abstract:
In this talk, we study the multiscale Boltzmann equation with multi-dimensional random parameters by a bi-fidelity stochastic collocation (SC) method developed before. 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. A priori estimate on the accuracy between the high-fidelity and bi-fidelity solutions in a more general framework of solving multi-scale kinetic equations (high-fidelity models) is established. Finally, extensive numerical experiments are presented to verify the efficiency and accuracy of our proposed method.
This is a joint work with Xueyu Zhu.
In this talk, we study the multiscale Boltzmann equation with multi-dimensional random parameters by a bi-fidelity stochastic collocation (SC) method developed before. 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. A priori estimate on the accuracy between the high-fidelity and bi-fidelity solutions in a more general framework of solving multi-scale kinetic equations (high-fidelity models) is established. Finally, extensive numerical experiments are presented to verify the efficiency and accuracy of our proposed method.
This is a joint work with Xueyu Zhu.
