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Accuracy and Convergence Studies of the Numerical Solution of Compressible Flow ProblemsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 1997 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Uppsala: Acta Universitatis Upsaliensis, 1997. , 17 p.
##### Series

Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1104-232X ; 316
##### Keyword [en]

computational fluid dynamics, Navier-Stokes equations, convergence acceleration, preconditioning, semi-implicit, multiblock, multigrid, finite volume method
##### National Category

Computational Mathematics
##### Research subject

Numerical Analysis
##### Identifiers

URN: urn:nbn:se:uu:diva-119ISBN: 91-554-4059-2OAI: oai:DiVA.org:uu-119DiVA: diva2:160743
##### Public defence

1997-11-07, Room 2347, Polacksbacken, Uppsala University, Uppsala, 10:15 (English)
#####

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#####

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Available from: 1997-10-17 Created: 1997-10-17 Last updated: 2015-06-03Bibliographically approved

The numerical solution of compressible flow problems governed by the Navier-Stokes equations is considered. A finite volume method is used for the discretization in space. Different techniques to accelerate the convergence to a steady state are suggested, and the accuracy of the spatial difference operator is analyzed.

By treating one spatial direction implicitly, it is possible to modify an explicit Runge-Kutta time-marching method, leading to a semi-implicit scheme. A thorough investigation of the stability and convergence properties is presented. Moreover, the scheme is used as a smoother in a multigrid method, and is reformulated as a preconditioner for a number of Newton-Krylov methods. The semi-implicit approach is shown to be very effective for meshes with high aspect ratios. For the flow over a flat plate with a thin boundary layer, the number of iterations to reach convergence is independent of the Reynolds number (*Re*).

An alternative approach for accelerating the convergence is to apply an optimal semicirculant approximation of the spatial operator as a preconditioner. Also here, significant speedups are demonstrated for high *Re* flows.

Two problems appearing for solvers used in computational fluid dynamics are examined. Methods for updating the ghost cells in a multigrid multiblock algorithm are studied, and the accuracy of the finite volume method applied to a polar mesh is analyzed. Although polar mesh singularities lead to a reduction of the order of the truncation error, the global error is shown to be of practically the same order as for a uniform mesh.

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