Comparison of nonlinear solvers within continuation method for steady-state variably saturated groundwater flow modeling

Nonlinearity continuation method, applied to boundary value problems for steady-state Richards equation, gradually approaches the solution through a series of intermediate problems. Originally, the Newton method with simple line search algorithm was used to solve the intermediate problems. In this paper, other solvers such as Picard and mixed Picard-Newton methods are considered, combined with slightly modified line search approach. Numerical experiments are performed with advanced finite volume discretizations on model and real-life problems.