Nonlinear multilevel iterative methods for multiscale models of air/water flow in porous media
Christopher E. Kees, Matthew W. Farthing, Lea Jenkins, C. T. Kelley, Stacy E. Howington, Kees, Chris · 2006
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 perfomance and solution accuracy, focusing particularly on the effects of degenerate coefficients in wetting and drying problems.