An Acoustic and Shock Wave Capturing Compact High-Order Gas-Kinetic Scheme with Spectral-Like Resolution

Abstract

A compact high-order gas-kinetic scheme (GKS) with spectral resolution will be presented and used in the simulation of acoustic and shock waves. Based on high-order gas evolution model, the GKS provides a time accurate solution at a cell interface, from which both time accurate flux function and flow variables can be obtained for updating cell averaged conservative flow variables and gradients. Based on cell-averaged flow variables and gradients, a reconstruction with compact stencil up to eighth-order spacial accuracy can be achieved, which include the nonlinear reconstruction for initial non-equilibrium state and linear reconstruction for the equilibrium one. The GKS unifies the nonlinear and linear reconstruction through a time evolution process at a cell interface from the non-equilibrium state to an equilibrium one. In the smooth acoustic wave region, the linear reconstruction will contribute mainly to the evolution. In the non-equilibrium shock region, the nonlinear reconstruction will play a dominant role.