thumbnail

Use of Picard and Newton iteration for solving nonlinear ground water flow equations

Ground Water

By:
DOI: 10.1111/j.1745-6584.2006.00207.x

Links

Abstract

This study examines the use of Picard and Newton iteration to solve the nonlinear, saturated ground water flow equation. Here, a simple three-node problem is used to demonstrate the convergence difficulties that can arise when solving the nonlinear, saturated ground water flow equation in both homogeneous and heterogeneous systems with and without nonlinear boundary conditions. For these cases, the characteristic types of convergence patterns are examined. Viewing these convergence patterns as orbits of an attractor in a dynamical system provides further insight. It is shown that the nonlinearity that arises from nonlinear head-dependent boundary conditions can cause more convergence difficulties than the nonlinearity that arises from flow in an unconfined aquifer. Furthermore, the effects of damping on both convergence and convergence rate are investigated. It is shown that no single strategy is effective for all problems and how understanding pitfalls and merits of several methods can be helpful in overcoming convergence difficulties. Results show that Picard iterations can be a simple and effective method for the solution of nonlinear, saturated ground water flow problems.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
Use of Picard and Newton iteration for solving nonlinear ground water flow equations
Series title:
Ground Water
DOI:
10.1111/j.1745-6584.2006.00207.x
Volume
44
Issue:
4
Year Published:
2006
Language:
English
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
First page:
583
Last page:
594
Number of Pages:
12