(untitled) (Communications in Computational Physics, 2019)
Due to its computational efficiency, high-order finite difference (FD) method is attractive, but the difficulty of treating boundary hampers the practical application in complex flow simulation. In this work, we propose a novel high-order FD scheme based on discontinuous Galerkin (DG) boundary treatment (FDbDG) where a DG method based on variational principle is applied to provide the flow properties in the vicinity of the boundary with desirable derivative information in time. In order to carefully combine the finite element and finite difference, Hermite weighted essentially non-oscillatory (HWENO) interpolation is adopted to build the HWENO flux for interior FD scheme and HWENO reconstruction is used to construct the degrees of freedom in the DG flux for boundary variational method. Several typical test cases are selected to evaluate the treatment for FD boundary. Numerical results show the proposed FDbDG method can reach arbitrary order of accuracy including boundary region with non-essentially oscillations.