arrow
Volume 32, Issue 4
High-Order Unified Gas-Kinetic Scheme

Gyuha Lim, Yajun Zhu & Kun Xu

Commun. Comput. Phys., 32 (2022), pp. 951-979.

Published online: 2022-10

Export citation
  • 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.

  • AMS Subject Headings

65M08, 65D05, 76P05, 82B40

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-32-951, author = {Lim , GyuhaZhu , Yajun and Xu , Kun}, title = {High-Order Unified Gas-Kinetic Scheme}, journal = {Communications in Computational Physics}, year = {2022}, volume = {32}, number = {4}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0113}, url = {http://global-sci.org/intro/article_detail/cicp/21135.html} }
TY - JOUR T1 - High-Order Unified Gas-Kinetic Scheme AU - Lim , Gyuha AU - Zhu , Yajun AU - Xu , Kun JO - Communications in Computational Physics VL - 4 SP - 951 EP - 979 PY - 2022 DA - 2022/10 SN - 32 DO - http://doi.org/10.4208/cicp.OA-2022-0113 UR - https://global-sci.org/intro/article_detail/cicp/21135.html KW - High-order reconstruction, two-stage fourth-order scheme, WENO-AO, micro flow. AB -

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.

Gyuha Lim, Yajun Zhu & Kun Xu. (2022). High-Order Unified Gas-Kinetic Scheme. Communications in Computational Physics. 32 (4). 951-979. doi:10.4208/cicp.OA-2022-0113
Copy to clipboard
The citation has been copied to your clipboard