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

TL;DR

This paper compares different nonlinear solvers, including Newton, Picard, and mixed methods, within a continuation framework for steady-state variably saturated groundwater flow modeling, demonstrating their effectiveness through numerical experiments.

Contribution

It introduces and evaluates alternative nonlinear solvers combined with a modified line search in the continuation method for groundwater flow problems.

Findings

Picard and mixed Picard-Newton methods perform comparably to Newton in certain scenarios.

Modified line search enhances solver stability and convergence.

Numerical experiments validate the effectiveness of alternative solvers on real-life problems.

Abstract

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.