On efficient simulation of non-Newtonian flow in saturated porous media with a multigrid adaptive refinement solver |
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Authors: | Oleg Iliev Daniela Vassileva Dimitar Stoyanov Willy Dörfler |
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Affiliation: | (1) Department of Mathematical Sciences, Clemson University, Clemson, SC 29634, USA;(2) The Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA |
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Abstract: | Flow of non-Newtonian fluid in saturated porous media can be described by the continuity equation and the generalized Darcy
law. Here we discuss the efficient solution of the resulting second order nonlinear elliptic equation. The equation is discretized
by the finite volume method on a cell-centered grid. Local adaptive refinement of the grid is introduced in order to reduce
the number of unknowns. We develop a special implementation, that 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 an 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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