General Synthetic Iterative Scheme for Unsteady Rarefied Gas Flows

General Synthetic Iterative Scheme for Unsteady Rarefied Gas Flows

Year:    2023

Author:    Jianan Zeng, Wei Su, Lei Wu

Communications in Computational Physics, Vol. 34 (2023), Iss. 1 : pp. 173–207

Abstract

In rarefied gas flows, the spatial grid size could vary by several orders of magnitude in a single flow configuration (e.g., inside the Knudsen layer it is at the order of mean free path of gas molecules, while in the bulk region it is at a much larger hydrodynamic scale). Therefore, efficient implicit numerical method is urgently needed for time-dependent problems. However, the integro-differential nature of gas kinetic equations poses a grand challenge, as the gain part of the collision operator is non-invertible. Hence an iterative solver is required in each time step, which usually takes a lot of iterations in the (near) continuum flow regime where the Knudsen number is small; worse still, the solution does not asymptotically preserve the fluid dynamic limit when the spatial cell size is not refined enough. Based on the general synthetic iteration scheme for steady-state solution of the Boltzmann equation, we propose two numerical schemes to push the multiscale simulation of unsteady rarefied gas flows to a new boundary, that is, the numerical solution not only converges within dozens of iterations in each time step, but also asymptotically preserves the Navier-Stokes-Fourier limit in the continuum flow regime, when the spatial grid is coarse, and the time step is large (e.g., in simulating the extreme slow decay of two-dimensional Taylor vortex, the time step is even at the order of vortex decay time). The properties of fast convergence and asymptotic preserving of the proposed schemes are not only rigorously proven by the Fourier stability analysis for simplified gas kinetic models, but also demonstrated by several numerical examples for the gas kinetic models and the Boltzmann equation.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2023-0068

Communications in Computational Physics, Vol. 34 (2023), Iss. 1 : pp. 173–207

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    35

Keywords:    Unsteady rarefied gas flow general synthetic iterative scheme fast convergence asymptotic Navier-Stokes preserving.

Author Details

Jianan Zeng

Wei Su

Lei Wu

  1. Multiscale simulation of rarefied gas dynamics via direct intermittent GSIS-DSMC coupling

    Luo, Liyan | Wu, Lei

    Advances in Aerodynamics, Vol. 6 (2024), Iss. 1

    https://doi.org/10.1186/s42774-024-00188-y [Citations: 0]
  2. A conservative implicit scheme for three-dimensional steady flows of diatomic gases in all flow regimes using unstructured meshes in the physical and velocity spaces

    Zhang, Rui | Liu, Sha | Chen, Jianfeng | Zhuo, Congshan | Zhong, Chengwen

    Physics of Fluids, Vol. 36 (2024), Iss. 1

    https://doi.org/10.1063/5.0186520 [Citations: 4]
  3. General synthetic iterative scheme for rarefied gas mixture flows

    Zeng, Jianan | Li, Qi | Wu, Lei

    Journal of Computational Physics, Vol. 519 (2024), Iss. P.113420

    https://doi.org/10.1016/j.jcp.2024.113420 [Citations: 1]
  4. Further acceleration of multiscale simulation of rarefied gas flow via a generalized boundary treatment

    Liu, Wei | Zhang, Yanbing | Zeng, Jianan | Wu, Lei

    Journal of Computational Physics, Vol. 503 (2024), Iss. P.112830

    https://doi.org/10.1016/j.jcp.2024.112830 [Citations: 7]
  5. An implicit adaptive unified gas-kinetic scheme for steady-state solutions of nonequilibrium flows

    Long, Wenpei | Wei, Yufeng | Xu, Kun

    Physics of Fluids, Vol. 36 (2024), Iss. 10

    https://doi.org/10.1063/5.0232275 [Citations: 0]
  6. Efficient parallel solver for rarefied gas flow using GSIS

    Zhang, Yanbing | Zeng, Jianan | Yuan, Ruifeng | Liu, Wei | Li, Qi | Wu, Lei

    Computers & Fluids, Vol. 281 (2024), Iss. P.106374

    https://doi.org/10.1016/j.compfluid.2024.106374 [Citations: 5]