Fourth-order gas-kinetic scheme for turbulence simulation with multi-dimensional WENO reconstruction

Abstract

In this paper, a fourth-order multi-dimensional weighted essentially non-oscillatory (WENO) reconstruction is developed, which is aiming at the complicated flows. In corporate with two-stage fourth-order temporal discretization, a high-order gas-kinetic scheme is proposed for the direct numerical simulation (DNS) and large eddy simulation (LES) of turbulence. In such WENO scheme, a simple strategy of selecting stencils is adopted and the topology independent linear weights are used. The fourth-order reconstruction improves the order of accuracy of the previous third-order WENO reconstruction [Computers and Fluids 198 (2020) 104401], which is too dissipative for the simulation of turbulent flows. Compared with the classical dimension-by-dimension WENO reconstruction, the order of accuracy can be also achieved for any non-uniform and curvilinear meshes in the finite volume framework. Numerical examples, including the classical turbulence cases, are provided to illustrate the good performance of such WENO scheme for turbulence simulation. More importantly, the fourth-order WENO scheme is robust and works well from the subsonic to hypersonic flows. In the future, the current scheme will be extended to the genuinely unstructured meshes for more complicated turbulent flows.