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A Particle Fokker-Planck Algorithm with Multiscale Temporal Discretization for Rarefied and Continuum Gas Flows

Published online by Cambridge University Press:  21 June 2017

Fei Fei,
Zhaohui Liu,
Jun Zhang and
Chuguang Zheng
Fei Fei*
Affiliation:
School of Aerospace Engineering, Huazhong University of Science and Technology, Wuhan 430074, P.R. ChinaState Key Laboratory of Coal Combustion, School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, P.R. China
Zhaohui Liu*
Affiliation:
State Key Laboratory of Coal Combustion, School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, P.R. China
Jun Zhang*
Affiliation:
School of Engineering, University of Edinburgh, Edinburgh EH9 3FB, United KingdomSchool of Aeronautic Science and Engineering, Beihang University, Beijing 100191, P.R. China
Chuguang Zheng*
Affiliation:
State Key Laboratory of Coal Combustion, School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, P.R. China
*
*Corresponding author. Email addresses:ffei@hust.edu.cn (F. Fei), zliu@hust.edu.cn (Z. Liu), jun.zhang@buaa.edu.cn (J. Zhang), cgzheng@hust.edu.cn (C. Zheng)
*Corresponding author. Email addresses:ffei@hust.edu.cn (F. Fei), zliu@hust.edu.cn (Z. Liu), jun.zhang@buaa.edu.cn (J. Zhang), cgzheng@hust.edu.cn (C. Zheng)
*Corresponding author. Email addresses:ffei@hust.edu.cn (F. Fei), zliu@hust.edu.cn (Z. Liu), jun.zhang@buaa.edu.cn (J. Zhang), cgzheng@hust.edu.cn (C. Zheng)
*Corresponding author. Email addresses:ffei@hust.edu.cn (F. Fei), zliu@hust.edu.cn (Z. Liu), jun.zhang@buaa.edu.cn (J. Zhang), cgzheng@hust.edu.cn (C. Zheng)

Abstract

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For gas flows with moderate and low Knudsen numbers, pair-wise collisions in the Boltzmann equation can be approximated by the Langevin model corresponding to the Fokker-Planck equation. Using this simplified collision model, particle numerical schemes, e.g. the Fokker-Planck model (FPM) method, can simulate low Knudsen number gas flows more efficient than those based on the Boltzmann equation, such as the Direct Simulation Monte Carlo (DSMC) method. However, as analyzed in this paper, the transport properties of the FPM method deviate from the physical values as the time step increases, and this problem affects its computational accuracy and efficiency for the simulation of multi-scale flows. Herewe propose a particle Fokker-Planck algorithm with multiscale temporal discretization (MTD-FPM) to overcome the drawbacks of the original FPM method. In the MTD-FPM method, the molecular motion is tracked following the integration scheme of the Langevin model in analogy to the original FPM method. However, to ensure consistent transport coefficients for arbitrary temporal discretization, a time step dependent friction coefficient has been implemented. Several benchmark problems, including Couette, thermal Couette, Poiseuille, and Sod tube flows, are simulated to validate the proposed MTD-FPM method.

Keywords

Particle simulation methodFokker-Planck modeltemporal discretizationmultiscale flow

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 2 , August 2017, pp. 338 - 374
Copyright
Copyright © Global-Science Press 2017 

Footnotes

Communicated by Kun Xu

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