TY - JOUR
T1 - High Order Finite Difference Scheme based on DG Boundary Treatment (FDbDG)
AU - Kun Wang, Jian Cheng & Tiegang Liu
JO - Communications in Computational Physics
VL - 5
SP - 1413
EP - 1445
PY - 2019
DA - 2019/01
SN - 25
DO - http://doi.org/10.4208/cicp.OA-2017-0088
UR - https://global-sci.org/intro/article_detail/cicp/12956.html
KW - Finite difference scheme, discontinuous Galerkin method, Hermite weighted essentially non-oscillatory schemes, boundary treatment.
AB - <p style="text-align: justify;">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.</p>