Advances in Aerodynamics

In this paper, a class of compact higher-order gas-kinetic schemes (GKS) with spectral-like resolution has been developed. Based on a time-dependent gas evolution model at a cell interface, the finite volume GKS updates both cell averaged conservative flow variables and their slopes through the fluxes and flow variables at the cell interface. As a result, the compact 6th- and 8th-order linear and nonlinear reconstructions can be obtained on a stencil of a second-order scheme. The time evolution model in GKS unifies the nonlinear and linear reconstructions through a relaxation process from non-equilibrium state to equilibrium one. To achieve a 4th-order time accuracy, based on the multi-stage multi-derivative (MSMD) formulation, the current higher-order GKS is time-stepping scheme with only one middle stage instead of 3 middle stages in the conventional 4th-order Runge-Kutta method. The time step used in the compact GKS can take a relative large CFL number(CFL≥0.3).  Many numerical tests have been used to validate the compact scheme in the capturing of solutions from strong shocks to aero-acoustic waves in both inviscid and viscous computations. The 6th- and 8th-order compact GKS provide a state-of-art high-order numerical schemes with robustness, accuracy, and efficiency for the compressible flow simulations. ​​​​​​​Read more.