Volume 5, Issue 2-4
A Discontinuous Galerkin Extension of the Vertex-Centered Edge-Based Finite Volume Method

Martin Berggren, Sven-Erik Ekström & Jan Nordström

Commun. Comput. Phys., 5 (2009), pp. 456-468.

Published online: 2009-02

Preview Full PDF 237 2016
Export citation
  • Abstract

The finite volume (FV) method is the dominating discretization technique for computational fluid dynamics (CFD), particularly in the case of compressible fluids. The discontinuous Galerkin (DG) method has emerged as a promising high-accuracy alternative. The standard DG method reduces to a cell-centered FV method at lowest order. However, many of today’s CFD codes use a vertex-centered FV method in which the data structures are edge based. We develop a new DG method that reduces to the vertex-centered FV method at lowest order, and examine here the new scheme for scalar hyperbolic problems. Numerically, the method shows optimal-order accuracy for a smooth linear problem. By applying a basic hp-adaption strategy, the method successfully handles shocks. We also discuss how to extend the FV edge-based data structure to support the new scheme. In this way, it will in principle be possible to extend an existing code employing the vertex-centered and edge-based FV discretization to encompass higher accuracy through the new DG method.

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-5-456, author = {}, title = {A Discontinuous Galerkin Extension of the Vertex-Centered Edge-Based Finite Volume Method}, journal = {Communications in Computational Physics}, year = {2009}, volume = {5}, number = {2-4}, pages = {456--468}, abstract = {

The finite volume (FV) method is the dominating discretization technique for computational fluid dynamics (CFD), particularly in the case of compressible fluids. The discontinuous Galerkin (DG) method has emerged as a promising high-accuracy alternative. The standard DG method reduces to a cell-centered FV method at lowest order. However, many of today’s CFD codes use a vertex-centered FV method in which the data structures are edge based. We develop a new DG method that reduces to the vertex-centered FV method at lowest order, and examine here the new scheme for scalar hyperbolic problems. Numerically, the method shows optimal-order accuracy for a smooth linear problem. By applying a basic hp-adaption strategy, the method successfully handles shocks. We also discuss how to extend the FV edge-based data structure to support the new scheme. In this way, it will in principle be possible to extend an existing code employing the vertex-centered and edge-based FV discretization to encompass higher accuracy through the new DG method.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7743.html} }
TY - JOUR T1 - A Discontinuous Galerkin Extension of the Vertex-Centered Edge-Based Finite Volume Method JO - Communications in Computational Physics VL - 2-4 SP - 456 EP - 468 PY - 2009 DA - 2009/02 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7743.html KW - AB -

The finite volume (FV) method is the dominating discretization technique for computational fluid dynamics (CFD), particularly in the case of compressible fluids. The discontinuous Galerkin (DG) method has emerged as a promising high-accuracy alternative. The standard DG method reduces to a cell-centered FV method at lowest order. However, many of today’s CFD codes use a vertex-centered FV method in which the data structures are edge based. We develop a new DG method that reduces to the vertex-centered FV method at lowest order, and examine here the new scheme for scalar hyperbolic problems. Numerically, the method shows optimal-order accuracy for a smooth linear problem. By applying a basic hp-adaption strategy, the method successfully handles shocks. We also discuss how to extend the FV edge-based data structure to support the new scheme. In this way, it will in principle be possible to extend an existing code employing the vertex-centered and edge-based FV discretization to encompass higher accuracy through the new DG method.

Martin Berggren, Sven-Erik Ekström & Jan Nordström. (2020). A Discontinuous Galerkin Extension of the Vertex-Centered Edge-Based Finite Volume Method. Communications in Computational Physics. 5 (2-4). 456-468. doi:
Copy to clipboard
The citation has been copied to your clipboard