Volume 25, Issue 5
High Order Finite Difference Scheme based on DG Boundary Treatment (FDbDG)

Kun Wang, Jian Cheng & Tiegang Liu

Commun. Comput. Phys., 25 (2019), pp. 1413-1445.

Published online: 2019-01

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  • Abstract

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.

  • Keywords

Finite difference scheme, discontinuous Galerkin method, Hermite weighted essentially non-oscillatory schemes, boundary treatment.

  • AMS Subject Headings

35Q30, 65M60, 76N15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-25-1413, author = {}, title = {High Order Finite Difference Scheme based on DG Boundary Treatment (FDbDG)}, journal = {Communications in Computational Physics}, year = {2019}, volume = {25}, number = {5}, pages = {1413--1445}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0088}, url = {http://global-sci.org/intro/article_detail/cicp/12956.html} }
TY - JOUR T1 - High Order Finite Difference Scheme based on DG Boundary Treatment (FDbDG) 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 -

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.

Kun Wang, Jian Cheng & Tiegang Liu. (2020). High Order Finite Difference Scheme based on DG Boundary Treatment (FDbDG). Communications in Computational Physics. 25 (5). 1413-1445. doi:10.4208/cicp.OA-2017-0088
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