Immersed boundary method based on high-order discontinuous Galerkin method

To decrease the difficulty of generating body-fitted meshes for complex geometries, the immersed boundary (IB) method based on Cartesian mesh has gradually become a popular numerical method for studying such problems in recent years. However, accuracy and efficiency of this method still need to be improved. Compared with the traditional finite volume scheme with second-order spatial accuracy, third-order or higher-order numerical methods have the advantages of high spatial accuracy, high numerical resolution and low numerical dissipation. However, the discontinuous Galerkin (DG) method, as one of the high-precision numerical methods, is still rarely applied with the immersed boundary. This paper proposes a high-order discontinuous Galerkin method for compressible flows by combining the advantage of the high-order discontinuous Galerkin method and the immersed boundary method. The boundary conditions in this paper are realized by the volume penalization method. Newton’s method iteration and MPI are used to improve computational efficiency. The inverse distance weight at interpolation point (IDW-IP) instead of the high-order polynomial defined in each element to perform high-order data reconstruction at the object surface. Based on the Cartesian grids, numerical tests are performed for two-dimensional steady and unsteady flows, and comparisons with those on traditional body-fitted grids are given.