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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Chen, Xi / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

IMPACT FACTOR 2017: 1.162

CiteScore 2017: 1.41

SCImago Journal Rank (SJR) 2017: 0.382
Source Normalized Impact per Paper (SNIP) 2017: 0.636

Mathematical Citation Quotient (MCQ) 2017: 0.12

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Volume 16, Issue 7-8


Numerical Solutions for Groundwater Flow in Unsaturated Layered Soil with Extreme Physical Property Contrasts

Chih-Yu Liu / Cheng-Yu Ku / Chi-Chao Huang / Der-Guey Lin / Wei-Chung Yeih
Published Online: 2015-11-17 | DOI: https://doi.org/10.1515/ijnsns-2015-0060


In this paper, the numerical solutions for groundwater flow in unsaturated layered soil using the Richards equation are presented. A linearisation process for the nonlinear Richards equation to deal with groundwater flow in unsaturated layered soil is derived. To solve one-dimensional flow in the unsaturated zone of layered soil profiles, flux conservation and the continuity of pressure potential at the interface between two consecutive layers are considered in the numerical model. In addition, a novel method, named the dynamical Jacobian-inverse free method, incorporated with a two-side equilibration algorithm for solving ill-conditioned systems with extreme contrasts in hydraulic conductivity is proposed. The validity of the model is established in numerous test problems by comparing the numerical results with the analytical solutions. The results show that the proposed method can improve convergence and numerical stability for solving groundwater flow in unsaturated layered soil with extreme contrasts in hydraulic conductivity.

Keywords: Richards equation; layered soil; ill-conditioned; nonlinear; hydraulic conductivity; groundwater flow

MSC® (2010).: 35J65; 65F22


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About the article

Received: 2015-05-12

Revised: 2015-09-10

Accepted: 2015-10-28

Published Online: 2015-11-17

Published in Print: 2015-12-01

Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 16, Issue 7-8, Pages 325–335, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2015-0060.

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