Nonlinear Multilevel Iterative Methods for Multiscale Models of Air/water Flow in Porous Media

Richards’ equation and the two-phase flow equations are well-known degenerate parabolic models of air/water flow in porous media. Poor iterative solver performance and small time steps during transient simulations are often reported in field-scale simulations. In this work we study Newton-multigrid and nonlinear multigrid methods applied to discrete air/water flow models. The models are discretized using standard continuous finite element spaces. Due to strong nonlinearity and potential degeneracy in the coefficients, we stabilize the models using a multiscale approach. We present computational results comparing iterative solver performance and solution accuracy, focusing particularly on the effects of degenerate coefficients in wetting and drying problems.