Gas-Kinetic Scheme With Space-Time Adaptive Mesh Refinement

Gas-kinetic scheme(GKS)is a new CFD method based on mesoscopic gas kinetic theory which has high accuracy and strong robustness in high-speed viscous flows.Combining GKS with unstructured mesh adaptive refinement(AMR)and time adaptive technologies,an efficient and robust GKS is developed,which can provide a powerful tool for numerical simulation of complex flows.Firstly,the AMR-GKS with second-order accurate in both space and time is developed by combining multidimensional GKS-NS flux solver with quadtree/octree unstructured grids adaptive framework P4 est.Considering that the global time step is too small when the refine level is large in unsteady flow,time adaptive technology is further introduced into AMR-GKS by using different size and number of time step on different grids,and the GKS with space-time adaptive mesh refinement(STAMR-GKS)is developed.Various typical tests,including steady/unsteady lid-driven cavity flows and shock interaction with SF6 column,are used to verify STAMR-GKS,and the computational efficiency is compared with the theoretical efficiency.The results show that,AMR significantly improves the efficiency of GKS,and STAMR-GKS further reduces the computational time while maintaining the computational accuracy.For the lid-driven cavity flow,which has less local large gradient(only near the upper corners),the advantage of STAMR is more significant.At the same time,due to the great dynamic load balancing of P4 est and the one-step characteristics of GKS,STAMR-GKS has a good parallel computing efficiency.Finally,the interaction of a shock wave and a SF6 bubble embedded with an air cavity is simulated by using STAMR-GKS.The shape of SF6 and air cavity,as well as the complex wave structures in flow fields are studied.Comparing with the results of no-cavity flow,it is found that the air cavity can destroy the convergence process of high-pressure transmission shock waves in SF6 bubble,and then inhibits the formation of jet structure.This work lays a good foundation for further research on the influence of air cavity shape and position.