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A vertex-centered discontinuous Galerkin method for flow problems
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
2016 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The understanding of flow problems, and finding their solution, has been important for most of human history, from the design of aqueducts to boats and airplanes. The use of physical miniature models and wind tunnels were, and still are, useful tools for design, but with the development of computers, an increasingly large part of the design process is assisted by computational fluid dynamics (CFD).

Many industrial CFD codes have their origins in the 1980s and 1990s, when the low order finite volume method (FVM) was prevalent. Discontinuous Galerkin methods (DGM) have, since the turn of the century, been seen as the successor of these methods, since it is potentially of arbitrarily high order. In its lowest order form DGM is equivalent to FVM. However, many existing codes are not compatible with standard DGM and would need a complete rewrite to obtain the advantages of the higher order.

This thesis shows how to extend existing vertex-centered and edge-based FVM codes to higher order, using a special kind of DGM discretization, which is different from the standard cell-centered type. Two model problems are examined to show the necessary data structures that need to be constructed, the order of accuracy for the method, and the use of an hp-adaptation scheme to resolve a developing shock. Then the method is further developed to solve the steady Euler equations, within the existing industrial Edge code, using acceleration techniques such as local time stepping and multigrid.

With the ever increasing need for more efficient and accurate solvers and algorithms in CFD, the modified DGM presented in this thesis could be used to help and accelerate the adoption of high order methods in industry.

Place, publisher, year, edition, pages
Uppsala University, 2016.
Series
Information technology licentiate theses: Licentiate theses from the Department of Information Technology, ISSN 1404-5117 ; 2016-003
National Category
Computational Mathematics Computer Science
Research subject
Scientific Computing with specialization in Numerical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-284321OAI: oai:DiVA.org:uu-284321DiVA: diva2:920155
Supervisors
Available from: 2016-02-01 Created: 2016-04-16 Last updated: 2017-08-31Bibliographically approved
List of papers
1. A discontinuous Galerkin extension of the vertex-centered edge-based finite volume method
Open this publication in new window or tab >>A discontinuous Galerkin extension of the vertex-centered edge-based finite volume method
2009 (English)In: Communications in Computational Physics, ISSN 1815-2406, E-ISSN 1991-7120, Vol. 5, 456-468 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Science
Identifiers
urn:nbn:se:uu:diva-17606 (URN)000263563600013 ()
Available from: 2008-08-01 Created: 2008-07-30 Last updated: 2017-12-08Bibliographically approved
2. Incorporating a discontinuous Galerkin method into the existing vertex-centered edge-based finite volume solver Edge
Open this publication in new window or tab >>Incorporating a discontinuous Galerkin method into the existing vertex-centered edge-based finite volume solver Edge
2010 (English)In: ADIGMA — A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications, Berlin: Springer-Verlag , 2010, 39-52 p.Chapter in book (Refereed)
Place, publisher, year, edition, pages
Berlin: Springer-Verlag, 2010
Series
Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 113
National Category
Computational Mathematics Computer Science
Identifiers
urn:nbn:se:uu:diva-134383 (URN)10.1007/978-3-642-03707-8_4 (DOI)
Available from: 2010-09-18 Created: 2010-11-24 Last updated: 2016-04-16Bibliographically approved
3. Agglomeration multigrid for the vertex-centered dual discontinuous Galerkin method
Open this publication in new window or tab >>Agglomeration multigrid for the vertex-centered dual discontinuous Galerkin method
2010 (English)In: ADIGMA — A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications, Berlin: Springer-Verlag , 2010, 301-308 p.Chapter in book (Refereed)
Place, publisher, year, edition, pages
Berlin: Springer-Verlag, 2010
Series
Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 113
National Category
Computational Mathematics Computer Science
Identifiers
urn:nbn:se:uu:diva-134384 (URN)10.1007/978-3-642-03707-8_21 (DOI)
Available from: 2010-09-18 Created: 2010-11-24 Last updated: 2016-04-16Bibliographically approved

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Ekström, Sven-Erik

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