High-Order Unified Gas-kinetic Scheme

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.