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A discontinuous Galerkin extension of the vertex-centered edge-based finite volume method
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. (UMIT)ORCID-id: 0000-0003-0473-3263
Department of Information Technology, Uppsala University.
Department of Information Technology, Uppsala University.
2009 (Engelska)Ingår i: Communications in Computational Physics, ISSN 1815-2406, Vol. 5, nr 2-4, s. 456-468Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
2009. Vol. 5, nr 2-4, s. 456-468
Nyckelord [en]
Discontinuous Galerkin methods, finite volume methods, dual mesh, vertex-centered, edge-based, CFD
Nationell ämneskategori
Beräkningsmatematik
Identifikatorer
URN: urn:nbn:se:umu:diva-40284OAI: oai:DiVA.org:umu-40284DiVA, id: diva2:399140
Tillgänglig från: 2011-02-21 Skapad: 2011-02-21 Senast uppdaterad: 2018-06-08

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