Nonlinearity continuation method for steady-state groundwater flow modeling in variably saturated conditions

TL;DR

This paper introduces a nonlinearity continuation method for solving steady-state groundwater flow in variably saturated conditions, demonstrating its effectiveness compared to pseudo-transient methods through various test cases and parallel computations.

Contribution

The paper presents a novel nonlinearity continuation approach for steady-state groundwater modeling, improving solution robustness and efficiency over traditional pseudo-transient methods.

Findings

The continuation method effectively solves nonlinear systems in groundwater flow modeling.

It outperforms pseudo-transient methods in convergence and computational efficiency.

Parallel computations enhance the method's scalability for large problems.

Abstract

Application of nonlinearity continuation method to numerical solution of steady-state groundwater flow in variably saturated conditions is presented. In order to solve the system of nonlinear equations obtained by finite volume discretization of steady-state Richards equation, a series of problems with increasing nonlinearity are solved using the Newton method. This approach is compared to pseudo-transient method on several test cases, including real site problems and involving parallel computations.