An adaptive solution strategy for Richards' equation

TL;DR

This paper introduces a robust iterative solver for Richards' equation that adaptively switches between L-scheme and Newton methods using a posteriori indicators, improving numerical solution efficiency.

Contribution

It presents a novel adaptive switching algorithm with reliable criteria for solving Richards' equation, enhancing robustness and speed over previous methods.

Findings

The solver effectively handles nonlinearities in Richards' equation.

Numerical examples demonstrate improved convergence and robustness.

The method is applicable to various spatial discretizations.

Abstract

Flow in variably saturated porous media is typically modelled by the Richards equation, a nonlinear elliptic-parabolic equation which is notoriously challenging to solve numerically. In this paper, we propose a robust and fast iterative solver for Richards' equation. The solver relies on an adaptive switching algorithm, based on rigorously derived a posteriori indicators, between two linearization methods: L-scheme and Newton. Although a combined L-scheme/Newton strategy was introduced previously in [List & Radu (2016)], here, for the first time we propose a reliable and robust criteria for switching between these schemes. The performance of the solver, which can be in principle applied to any spatial discretization and linearization methods, is illustrated through several numerical examples.