First-order continuation method for steady-state variably saturated groundwater flow modeling

TL;DR

This paper explores an advanced predictor technique within the nonlinearity continuation method to improve steady-state Richards equation solutions, demonstrating its effectiveness through numerical experiments on diverse problems.

Contribution

It introduces a more sophisticated predictor in the continuation method for steady-state Richards equation, enhancing solution accuracy and robustness.

Findings

Improved solution convergence with the new predictor.

Effective application on real-life groundwater flow problems.

Compatibility with finite volume and mimetic finite difference methods.

Abstract

Recently, the nonlinearity continuation method has been used to numerically solve boundary value problems for steady-state Richards equation. The method can be considered as a predictor-corrector procedure with the simplest form which has been applied to date having a trivial, zeroth-order predictor. In this article, effect of a more sophisticated predictor technique is examined. Numerical experiments are performed with finite volume and mimetic finite difference discretizations on various problems, including real-life examples.