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Wed, 23 Nov 2005 14:29:15 +0100Wed, 23 Nov 2005 14:29:15 +0100On Efficent Simulation of Non-Newtonian Flow in Saturated Porous Media with a Multigrid Adaptive Refinement Solver
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1683
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.W. Dörfler; O. Iliev; D. Stoyanov; D. Vassilevareporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1683Wed, 23 Nov 2005 14:29:15 +0100Multigrid – adaptive local refinement solver for incompressible flows
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1511
A non-linear multigrid solver for incompressible Navier-Stokes equations, exploiting finite volume discretization of the equations, is extended by adaptive local refinement. The multigrid is the outer iterative cycle, while the SIMPLE algorithm is used as a smoothing procedure. Error indicators are used to define the refinement subdomain. A special implementation approach is used, which allows to perform unstructured local refinement in conjunction with the finite volume discretization. The multigrid - adaptive local refinement algorithm is tested on 2D Poisson equation and further is applied to a lid-driven flows in a cavity (2D and 3D case), comparing the results with bench-mark data. The software design principles of the solver are also discussed.O. Iliev; D. Stoyanovreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1511Tue, 10 Feb 2004 10:12:45 +0100On a Multigrid Adaptive Refinement Solver for Saturated Non-Newtonian Flow in Porous Media
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1509
On a Multigrid Adaptive Refinement Solver for Saturated Non-Newtonian Flow in Porous Media A multigrid adaptive refinement algorithm for non-Newtonian flow in porous media is presented. The saturated flow of a non-Newtonian fluid is described by the continuity equation and the generalized Darcy law. The resulting second order nonlinear elliptic equation is discretized by a finite volume method on a cell-centered grid. A nonlinear full-multigrid, full-approximation-storage algorithm is implemented. As a smoother, a single grid solver based on Picard linearization and Gauss-Seidel relaxation is used. Further, a local refinement multigrid algorithm on a composite grid is developed. A residual based error indicator is used in the adaptive refinement criterion. A special implementation approach is used, which allows us to perform unstructured local refinement in conjunction with the finite volume discretization. Several results from numerical experiments are presented in order to examine the performance of the solver.W. Dörfler; O. Iliev; D. Stoyanov; D. Vassilevareporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1509Tue, 10 Feb 2004 10:06:38 +0100