High-order compact gas-kinetic schemes for three-dimensional flow simulations on tetrahedral mesh

A general framework for the development of high-order compact schemes has been proposed recently.The core steps of the schemes are composed of the following.1).Based on a kinetic model equation,from a generalized initial distribution of flow variables construct a time-accurate evolution solution of gas distribution function at a cell interface and obtain the corresponding flux function;2).Introduce the WENO-type weighting functions into the high-order time-derivative of the cell interface flux function in the multistage multi-derivative(MSMD)time stepping scheme to cope with the possible impingement of a shock wave on a cell interface within a time step,and update the cell-averaged conservative flow variables inside each control volume;3).Model the time evolution of the gas distribution function on both sides of a cell interface separately,take moments of the inner cell interface gas distribution function to get flow variables,and update the cell-averaged gradients of flow variables inside each control volume;4).Based on the cell-averaged flow variables and their gradients,develop compact initial data reconstruction to get initial condition of flow distributions at the beginning of next time step.A compact gas-kinetic scheme(GKS)up to sixth-order accuracy in space and fourth-order in time has been constructed on 2D unstructured mesh.In this paper,the compact GKS up to fourth-order accuracy on three-dimensional tetrahedral mesh will be further constructed with the focus on the WENO-type initial compact data reconstruction.Nonlinear weights are designed to achieve high-order accuracy for the smooth Navier-Stokes solution and keep super robustness in 3D computation with strong shock interactions.The fourth-order compact GKS uses a large time step with a CFL number 0.6 in the simulations from subsonic to hypersonic flow.A series of test cases are used to validate the scheme.The high-order compact GKS can be used in 3D applications with complex geometry.