On Efficent Simulation of Non-Newtonian Flow in Saturated Porous Media with a Multigrid Adaptive Refinement Solver

  • Flow of non-Newtonian fluid in saturated porous media can be described by the continuity equation and the generalized Darcy law. Efficient solution of the resulting second order nonlinear elliptic equation is discussed here. The equation is discretized by a finite volume method on a cell-centered grid. Local adaptive refinement of the grid is introduced in order to reduce the number of unknowns. A special implementation approach is used, which allows us to perform unstructured local refinement in conjunction with the finite volume discretization. Two residual based error indicators are exploited in the adaptive refinement criterion. Second order accurate discretization of the fluxes on the interfaces between refined and non-refined subdomains, as well as on the boundaries with Dirichlet boundary condition, are presented here, as an essential part of the accurate and efficient algorithm. A nonlinear full approximation storage multigrid algorithm is developed especially for the above described composite (coarse plus locally refined) grid approach. In particular, second order approximation of the fluxes around interfaces is a result of a quadratic approximation of slave nodes in the multigrid - adaptive refinement (MG-AR) algorithm. Results from numerical solution of various academic and practice-induced problems are presented and the performance of the solver is discussed.

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Verfasserangaben:W. Dörfler, O. Iliev, D. Stoyanov, D. Vassileva
URN (Permalink):urn:nbn:de:hbz:386-kluedo-13989
Schriftenreihe (Bandnummer):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (70)
Sprache der Veröffentlichung:Englisch
Jahr der Fertigstellung:2005
Jahr der Veröffentlichung:2005
Veröffentlichende Institution:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Datum der Publikation (Server):23.11.2005
Freies Schlagwort / Tag:Nonlinear multigrid; adaptive refinement; non-Newtonian flow in porous media
Fachbereiche / Organisatorische Einheiten:Fraunhofer (ITWM)
DDC-Sachgruppen:5 Naturwissenschaften und Mathematik / 510 Mathematik
Lizenz (Deutsch):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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