Advanced Solver Methods for Subsurface Environmental Problems

The present report outlines recent results relative to the development of new linear and nonlinear approaches for solving groundwater flow problems. Efficient and robust simulation of complex processes in environmental applications is crucial for understanding, forecasting and performing opportune and reliable decisions. This research effort focuses in developing efficient solvers for two main models in groundwater flow: Richards’ equation and air-water coupled equation systems. To achieve this goal, two main streams of research are presented:(a) High-order Newton-Krylov methods, and (b) Decoupling and constraint operators for preconditioning coupled systems of nonlinear equations. Numerical results reveal that these approaches have high potentials for dealing with stringent physical situations.