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A discontinuous Galerkin extension of the vertex-centered edge-based finite volume method
Umeå University, Faculty of Science and Technology, Department of Computing Science. (UMIT)
Department of Information Technology, Uppsala University.
Department of Information Technology, Uppsala University.
2009 (English)In: Communications in Computational Physics, ISSN 1815-2406, Vol. 5, no 2-4, 456-468 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2009. Vol. 5, no 2-4, 456-468 p.
Keyword [en]
Discontinuous Galerkin methods, finite volume methods, dual mesh, vertex-centered, edge-based, CFD
URN: urn:nbn:se:umu:diva-40284OAI: diva2:399140
Available from: 2011-02-21 Created: 2011-02-21 Last updated: 2011-12-28Bibliographically approved

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