High-Order Unified Gas-Kinetic Scheme (Communications in Computational Physics, 2022)
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 microscopicdistribution 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 appliedin the continuum flow simulation with complex structures, and that the rarefied flowstructure is usually smooth in the physical space, we apply the high-order techniquesin 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 thata balance of computational cost and numerical accuracy could be well achieved. TheHUGKS has been validated by several numerical test cases, including sine-wave accuracy test, Sod-shock tube, Couette, oscillating Couette, lid-driven cavity and oscillatingcavity flow. It is shown that the current method preserves the multiscale property ofthe original UGKS and obtains accurate solutions in the near continuum regimes.
Keywords: High-order reconstruction; two-stage fourth-order scheme; WENO-AO; micro flow.