For the numerical simulation of compressible flows,normally different mesh sizes are expected in different regions.For example,smaller mesh sizes are required to improve the local numerical resolution in the regions where the physical variables vary violently(for example,near the shock waves or in the boundary layers)and larger elements are expected for the regions where the solution is smooth.h-adaptive mesh has been widely used for complex flows.However,there are two difficulties when employing h-adaptivity for high-order discontinuous Galerkin(DG)methods.First,locally curved elements are required to precisely match the solid boundary,which significantly increases the difficulty to conduct the"refining"and"coarsening"operations since the curved information has to be maintained.Second,h-adaptivity could break the partition balancing,which would significantly affect the efficiency of parallel computing.In this paper,a robust and automatic h-adaptive method is developed for high-order DG methods on locally curved tetrahedral mesh,for which the curved geometries are maintained during the h-adaptivity.Furthermore,the reallocating and rebalancing of the computational loads on parallel clusters are conducted to maintain the parallel efficiency.Numerical results indicate that the introduced h-adaptive method is able to generate more reasonable mesh according to the structure of flow-fields.
