High-Order Unified Gas-Kinetic Scheme

High-Order Unified Gas-Kinetic Scheme

Year:    2022

Author:    Gyuha Lim, Yajun Zhu, Kun Xu

Communications in Computational Physics, Vol. 32 (2022), Iss. 4 : pp. 951–979

Abstract

In this paper, we present a high-order unified gas-kinetic scheme (UGKS) using the weighted essentially non-oscillatory with adaptive-order (WENO-AO) method for spatial reconstruction and the two-stage fourth-order scheme for time evolution. Since the UGKS updates both the macroscopic flow variables and microscopic distribution function, and provides an adaptive flux function by combining the equilibrium and non-equilibrium parts, it is possible to take separate treatment of the equilibrium and non-equilibrium calculation in the UGKS for the development of high-order scheme. Considering the fact that high-order techniques are commonly applied in the continuum flow simulation with complex structures, and that the rarefied flow structure is usually smooth in the physical space, we apply the high-order techniques in the equilibrium part of the UGKS for the capturing of macroscopic flow evolution, and retain the calculation of distribution function as a second-order method, so that a balance of computational cost and numerical accuracy could be well achieved. The HUGKS has been validated by several numerical test cases, including sine-wave accuracy test, Sod-shock tube, Couette, oscillating Couette, lid-driven cavity and oscillating cavity flow. It is shown that the current method preserves the multiscale property of the original UGKS and obtains accurate solutions in the near continuum regimes.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2022-0113

Communications in Computational Physics, Vol. 32 (2022), Iss. 4 : pp. 951–979

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    29

Keywords:    High-order reconstruction two-stage fourth-order scheme WENO-AO micro flow.

Author Details

Gyuha Lim

Yajun Zhu

Kun Xu