High-Order Unified Gas-kinetic Scheme  

作　　者：Gyuha Lim Yajun Zhu Kun Xu 

机构地区：[1]Department of Mechanical and Aerospace Engineering,The Hong Kong University of Science and Technology,Clear Water Bay,Kowloon,Hong Kong,China [2]Department of Mathematics,The Hong Kong University of Science and Technology,Clear Water Bay,Kowloon,Hong Kong,China [3]Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications,Hong Kong University of Science and Technology,Hong Kong,China [4]Shenzhen Research Institute,Hong Kong University of Science and Technology,Shenzhen,China

出　　处：《Communications in Computational Physics》2022年第9期951-979,共29页计算物理通讯（英文）

基　　金：supported by National Science Foundation of China(12172316);China Hong Kong Research Grant Council(16208021);Department of Science and Technology of Guangdong Province(Grant No.2020B1212030001).

摘　　要：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 highorder 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.

关 键 词：High-order reconstruction two-stage fourth-order scheme WENO-AO micro flow 

分 类 号：O17[理学—数学]