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A full approximation scheme (FAS) nonlinear multigrid solver for two-phaseflow and transport problems driven by wells with multiple perforations isdeveloped. It is an extension to our previous work on FAS solvers for diffusionand transport problems. The solver is applicable to discrete problems definedon unstructured grids as the coarsening algorithm is aggregation-based andalgebraic. To construct coarse basis that can better capture the radial flownear wells, coarse grids in which perforated well cells are not near thecoarse-element interface are desired. This is achieved by an aggregationalgorithm proposed in this paper that makes use of the location of well cellsin the cell-connectivity graph. Numerical examples in which the FAS solver iscompared against Newton's method on benchmark problems are given. Inparticular, for a refined version of the SAIGUP model, the FAS solver is atleast 35% faster than Newton's method for time steps with a CFL number greaterthan 10.

Multilevel well modeling in aggregation-based nonlinear multigrid for multiphase flow in porous media