Gas-kinetic scheme with space-time adaptive mesh refinement

Abstract The gas-kinetic scheme (GKS) is based on the mesoscopic gas-kinetic theory and can achieve a good balance between accuracy and robustness in a wide range of flows. In this study, a new GKS with space-time adaptive mesh refinement (STAMR-GKS) is developed for the Navier–Stokes equations on quadtree and octree structure grids by combining an AMR framework and a second-order accurate multidimensional GKS flux solver. STAMR-GKS can automatically adjust the mesh size according to local flow structures and significantly reduce the number of grid cells. Meanwhile, different time steps are used for cells of different refinement levels. Thus, the computational cost is further reduced effectively when compared with AMR-GKS using a global time step. Theoretical formulas are derived to measure the computation reduction of AMR and STAMR, which are based on the maximum refinement level and proportion of the finest cell number. The developed schemes are explicit and single-stage. Because of the special mesh-sorting method for tree structure data in the original framework, efficient dynamic load balancing is achieved in AMR-GKS. Considering that finer cells advance more steps in STAMR-GKS, a special strategy is proposed in which coarse cells surrounded by same-refinement-level cells can be updated without waiting for fine cells, thereby effectively improving the parallel efficiency. The strong robustness, high efficiency, and good parallel performance of the proposed schemes are validated by typical numerical tests involving singularity, shock waves and fluid interfaces, such as lid-driven cavity flows, shock-sulfur hexafluoride (SF6) cylinder and shock-SF6 sphere interaction flows.