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A nonlinear multigrid solver for two-phase flow and transport in a mixedfractional-flow velocity-pressure-saturation formulation is proposed. Thesolver, which is under the framework of the full approximation scheme (FAS),extends our previous work on nonlinear multigrid for heterogeneous diffusionproblems. The coarse spaces in the multigrid hierarchy are constructed by firstaggregating degrees of freedom, and then solving some local flow problems. Themixed formulation and the choice of coarse spaces allow us to assemble thecoarse problems without visiting finer levels during the solving phase, whichis crucial for the scalability of multigrid methods. Specifically, a naturalgeneralization of the upwind flux can be evaluated directly on coarse levelsusing the precomputed coarse flux basis vectors. The resulting solver isapplicable to problems discretized on general unstructured grids. Theperformance of the proposed nonlinear multigrid solver in comparison with thestandard single level Newton's method is demonstrated through challengingnumerical examples. It is observed that the proposed solver is robust forhighly nonlinear problems and clearly outperforms Newton's method in the caseof high Courant-Friedrichs-Lewy (CFL) numbers.

An Aggregation-based Nonlinear Multigrid Solver for Two-phase Flow and Transport in Porous Media