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

Liu Fengnan, Yasuhide Fukumoto, Xiaopeng Zhao

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

The Richards equation is a degenerate nonlinear PDE that models a flow through saturated/unsaturated porous media. Research on its numerical methods has been conducted in many fields. Implicit schemes based on a backward Euler format are widely used in calculating it. However, it is difficult to obtain stability with a numerical scheme because of the strong nonlinearity and degeneracy. In this paper, we establish a linearized semi-implicit finite difference scheme that is faster than backward Euler implicit schemes. We analyze the stability of this scheme by adding a small positive perturbation ϵ to the coefficient function of the Richards equation. Moreover, we show that there is a linear relationship between the discretization error in the L-norm and ϵ. Numerical experiments are carried out to verify our main results.

Original languageEnglish
Article number16
JournalJournal of Scientific Computing
Volume83
Issue number1
DOIs
Publication statusPublished - Apr 1 2020

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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