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 non-Newtonian fluid is described by continuity equation and generalized Darcy law. The resulting second order nonlinear elliptic equation is discretized by finite volume method on cell-centered grid. A nonlinear full-multigrid, full-approximation-storage algorithm is implemented. Singe grid solver, based on Picard linearization and Gauss-Seidel relaxation, is used as a smoother. 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