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A two-grid method for coupled free flow with porous media flow |
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| Authors: | Prince ChidyagwaiBéatrice Rivière |
| Institution: | a Department of Mathematics, Temple University, 1805 N. Broad Street, Philadelphia, PA 19122, USA b Department of Computational and Applied Mathematics, Rice University, 6100 Main Street, Houston, TX 77005, USA |
| Abstract: | This paper presents a two-grid method for solving systems of partial differential equations modelling incompressible free flow coupled with porous media flow. This work considers both the coupled Stokes and Darcy as well as the coupled Navier-Stokes and Darcy problems. The numerical schemes proposed are based on combinations of the continuous finite element method and the discontinuous Galerkin method. Numerical errors and convergence rates for solutions obtained from the two-grid method are presented. CPU times for the two-grid algorithm are shown to be significantly less than those obtained by solving the fully coupled problem. |
| Keywords: | Navier-Stokes equations Darcy&rsquo s law Discontinuous Galerkin Finite element method Beavers-Joseph-Saffman Decoupled and linearized problems |
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