A Finite Difference Scheme for the Richards Equation Under Variable-Flux Boundary

Yasuhide Fukumoto, Fengnan Liu, Xiaopeng Zhao

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The Richards equation is a degenerate nonlinear partial differential equation which serves as a model for describing a flow of water through saturated/unsaturated porous medium under the action of gravity. This paper develops a numerical method, with a mathematical support, for the one-dimensional Richards equation. Implicit schemes based on a backward Euler format have been widely used, but have a difficulty in insuring the stability, because of the strong nonlinearity and degeneracy. A linearized semi-implicit finite difference scheme that is faster than the backward Euler implicit schemes is established, the stability of this scheme is proved by adding a small perturbation to the coefficient function, and an error estimate is made. It is found that there is a linear relationship between the discretization error in a certain norm and the perturbation strength.

Original languageEnglish
Title of host publicationAdvances in Sustainable Construction and Resource Management
EditorsHemanta Hazarika, Gopal Santana Madabhushi, Kazuya Yasuhara, Dennes T. Bergado
PublisherSpringer Science and Business Media Deutschland GmbH
Pages231-245
Number of pages15
ISBN (Print)9789811600760
DOIs
Publication statusPublished - 2021
Event1st International Symposium on Construction Resources for Environmentally Sustainable Technologies, CREST 2020 - Fukuoka, Japan
Duration: Mar 9 2021Mar 11 2021

Publication series

NameLecture Notes in Civil Engineering
Volume144 LNCE
ISSN (Print)2366-2557
ISSN (Electronic)2366-2565

Conference

Conference1st International Symposium on Construction Resources for Environmentally Sustainable Technologies, CREST 2020
Country/TerritoryJapan
CityFukuoka
Period3/9/213/11/21

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering

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