High-order gas-kinetic scheme on three-dimensional unstructured meshes for compressible flows

Abstract

In this paper, a high-order gas-kinetic scheme is developed on three-dimensional unstructured meshes for compressible Euler and Navier–Stokes equations. To achieve the high-order spatial accuracy, the three-dimensional weighted essentially non-oscillatory (WENO) reconstruction is extended to the unstructured tetrahedral and hexahedral meshes. A simple strategy is adopted for the selection of candidate stencils, and the topologically independent linear weights are used for the spatial reconstruction. The efficiency and robustness of the classical WENO reconstruction are improved. In addition to the two-stage fourth-order temporal discretization and lower–upper symmetric Gauss–Seidel method, the explicit and implicit high-order gas-kinetic schemes are developed for unsteady and steady problems. Accuracy tests on hexahedral and tetrahedral grids validate the third-order of accuracy, and various three-dimensional incompressible and compressible numerical experiments are also presented. The results validate the accuracy and robustness of the proposed scheme for both inviscid and viscous flows. In the future, the current scheme will be extended to the hybrid unstructured meshes and Reynolds-averaged Navier–Stokes simulation with high Reynolds numbers.