High Order Finite Difference Scheme based on DG Boundary Treatment (FDbDG) (Communications in Computational Physics, 2019)
Due to its computational efficiency, high-order finite difference (FD) methodis attractive, but the difficulty of treating boundary hampers the practical application in complex flow simulation. In this work, we propose a novel high-order FDscheme based on discontinuous Galerkin (DG) boundary treatment (FDbDG) where aDG method based on variational principle is applied to provide the flow properties inthe vicinity of the boundary with desirable derivative information in time. In orderto carefully combine the finite element and finite difference, Hermite weighted essentially non-oscillatory (HWENO) interpolation is adopted to build the HWENO fluxfor interior FD scheme and HWENO reconstruction is used to construct the degreesof freedom in the DG flux for boundary variational method. Several typical test casesare selected to evaluate the treatment for FD boundary. Numerical results show theproposed FDbDG method can reach arbitrary order of accuracy including boundaryregion with non-essentially oscillations.
Keywords: Finite difference scheme; discontinuous Galerkin method; Hermite weighted essentially non-oscillatory schemes; boundary treatment.