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Hybrid Methods for Unsteady Fluid Flow Problems in Complex Geometries
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. (Waves and Fluids)
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 [en]
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: urn:nbn:se:uu:diva-8341ISBN: 978-91-554-7046-3 (print)OAI: oai:DiVA.org:uu-8341DiVA: diva2:171143
Public defence
2007-12-20, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2007-11-29 Created: 2007-11-29 Last updated: 2011-10-27Bibliographically approved
List of papers
1. Stable artificial dissipation operators for finite volume schemes on unstructured grids
Open this publication in new window or tab >>Stable artificial dissipation operators for finite volume schemes on unstructured grids
2006 (English)In: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 56, 1481-1490 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Science
Identifiers
urn:nbn:se:uu:diva-82053 (URN)10.1016/j.apnum.2005.11.002 (DOI)000241005200001 ()
Available from: 2006-10-28 Created: 2006-10-28 Last updated: 2011-11-29Bibliographically approved
2. A stable and efficient hybrid method for aeroacoustic sound generation and propagation
Open this publication in new window or tab >>A stable and efficient hybrid method for aeroacoustic sound generation and propagation
2005 (English)In: Comptes rendus. Mecanique, ISSN 1631-0721, Vol. 333, 713-718 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Science
Identifiers
urn:nbn:se:uu:diva-76225 (URN)10.1016/j.crme.2005.07.011 (DOI)
Available from: 2007-01-26 Created: 2007-01-26 Last updated: 2011-11-29Bibliographically approved
3. A stable hybrid method for hyperbolic problems
Open this publication in new window or tab >>A stable hybrid method for hyperbolic problems
2006 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 212, 436-453 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Science
Identifiers
urn:nbn:se:uu:diva-76226 (URN)10.1016/j.jcp.2005.07.008 (DOI)000234120100004 ()
Available from: 2006-10-28 Created: 2006-10-28 Last updated: 2016-01-28Bibliographically approved
4. A hybrid method for unsteady inviscid fluid flow
Open this publication in new window or tab >>A hybrid method for unsteady inviscid fluid flow
Show others...
2009 (English)In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 38, 875-882 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Science
Identifiers
urn:nbn:se:uu:diva-96535 (URN)10.1016/j.compfluid.2008.09.010 (DOI)000264305000014 ()
Available from: 2007-11-29 Created: 2007-11-29 Last updated: 2011-11-30Bibliographically approved
5. Stable, Accurate and Efficient Interface Procedures for Viscous Problems
Open this publication in new window or tab >>Stable, Accurate and Efficient Interface Procedures for Viscous Problems
2006 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2006-019
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-80176 (URN)
Available from: 2008-02-09 Created: 2008-02-09 Last updated: 2011-11-18Bibliographically approved
6. A stable and efficient hybrid scheme for viscous problems in complex geometries
Open this publication in new window or tab >>A stable and efficient hybrid scheme for viscous problems in complex geometries
2007 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 226, 1291-1309 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Science
Identifiers
urn:nbn:se:uu:diva-11185 (URN)10.1016/j.jcp.2007.05.018 (DOI)000250209700006 ()
Available from: 2007-09-21 Created: 2007-09-21 Last updated: 2011-11-30Bibliographically approved
7. A Hybrid Method for the Unsteady Compressible Navier-Stokes Equations
Open this publication in new window or tab >>A Hybrid Method for the Unsteady Compressible Navier-Stokes Equations
2007 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2007-029
National Category
Computational Mathematics Computer Science
Identifiers
urn:nbn:se:uu:diva-11803 (URN)
Available from: 2007-10-20 Created: 2007-10-20 Last updated: 2011-11-18Bibliographically approved

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