A Reconstructed Discontinuous Galerkin Method Based on a Hierarchical Hermite WENO Reconstruction for Compressible Flows on Tetrahedral Grids

A hierarchical Hermite WENO reconstruction-based discontinuous Galerkin method, designed not only to enhance the accuracy of discontinuous Galerkin method but also to avoid spurious oscillation in the vicinity of discontinuities, is developed for compressible flows on tetrahedral grids. In this method, a quadratic polynomial solution is first reconstructed from the underlying linear polynomial discontinuous Galerkin solution using a least-squares method. A Hermite WENO reconstruction is then performed to obtain the final representation of the quadratic polynomial solution. The developed RDG method is used to compute a variety of flow problems on tetrahedral meshes. The numerical experiments demonstrate that this Hermite WENO reconstruction-based RDG(P1P2) method is able to achieve the designed third-order accuracy, and outperforms the third-order DG method DG(P2) in terms of both computing costs and storage requirements