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A hybrid method for unsteady inviscid fluid flow
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.
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2009 (English)In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 38, 875-882 p.Article in journal (Refereed) Published
Place, publisher, year, edition, pages
2009. Vol. 38, 875-882 p.
National Category
Computational Mathematics Computer Science
Identifiers
URN: urn:nbn:se:uu:diva-96535DOI: 10.1016/j.compfluid.2008.09.010ISI: 000264305000014OAI: oai:DiVA.org:uu-96535DiVA: diva2:171140
Available from: 2007-11-29 Created: 2007-11-29 Last updated: 2011-11-30Bibliographically approved
In thesis
1. Hybrid Methods for Unsteady Fluid Flow Problems in Complex Geometries
Open this publication in new window or tab >>Hybrid Methods for Unsteady Fluid Flow Problems in Complex Geometries
2007 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis, stable and efficient hybrid methods which combine high order finite difference methods and unstructured finite volume methods for time-dependent initial boundary value problems have been developed. The hybrid methods make it possible to combine the efficiency of the finite difference method and the flexibility of the finite volume method.

We carry out a detailed analysis of the stability of the hybrid methods, and in particular the stability of interface treatments between structured and unstructured blocks. Both the methods employ so called summation-by-parts operators and impose boundary and interface conditions weakly, which lead to an energy estimate and stability.

We have constructed and analyzed first-, second- and fourth-order Laplacian based artificial dissipation operators for finite volume methods on unstructured grids. The first-order artificial dissipation can handle shock waves, and the fourth-order artificial dissipation eliminates non-physical numerical oscillations efficiently.

A stable hybrid method for hyperbolic problems has been developed. It is shown that the stability at the interface can be obtained by modifying the dual grid of the unstructured finite volume method close to the interface. The hybrid method is applied to the Euler equation by the coupling of two stand-alone CFD codes. Since the coupling is administered by a third separate coupling code, the hybrid method allows for individual development of the stand-alone codes. It is shown that the hybrid method is an accurate, efficient and practically useful computational tool that can handle complex geometries and wave propagation phenomena.

Stable and accurate interface treatments for the linear advection–diffusion equation have been studied. Accurate high-order calculation are achieved in multiple blocks with interfaces. Three stable interface procedures — the Baumann–Oden method, the “borrowing” method and the local discontinuous Galerkin method, have been investigated. The analysis shows that only minor differences separate the different interface handling procedures.

A conservative stable and efficient hybrid method for a parabolic model problem has been developed. The hybrid method has been applied to the full Navier–Stokes equations. The numerical experiments support the theoretical conclusions and show that the interface coupling is stable and converges at the correct order for the Navier–Stokes equations.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2007. 28 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 374
Keyword
hybrid methods, finite difference methods, finite volume methods, coupling procedure, stability, efficiency, artificial dissipation
National Category
Computational Mathematics
Research subject
Scientific Computing with specialization in Numerical Analysis
Identifiers
urn:nbn:se:uu:diva-8341 (URN)978-91-554-7046-3 (ISBN)
Public defence
2007-12-20, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 10:15 (English)
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Available from: 2007-11-29 Created: 2007-11-29 Last updated: 2011-10-27Bibliographically approved

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Nordström, JanMattsson, KenGong, Jing

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