An aggregation-based nonlinear multigrid solver for two-phase flow and transport in porous media

A nonlinear multigrid solver for two-phase flow and transport in a mixed fractional-flow velocity-pressure-saturation formulation is proposed. The solver, which under the framework of full approximation scheme (FAS), extends our previous work on heterogeneous diffusion problems. coarse spaces hierarchy are constructed by first aggregating degrees freedom, then solving some local choice allow us to assemble problems without visiting finer levels during phase, crucial scalability methods. Specifically, natural generalization upwind flux can be evaluated directly using precomputed basis vectors. resulting applicable discretized general unstructured grids. performance proposed comparison with standard single level Newton's method demonstrated through challenging numerical examples. It observed that robust highly clearly outperforms case high Courant-Friedrichs-Lewy (CFL) numbers.