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

Liu Fengnan, Yasuhide Fukumoto, Xiaopeng Zhao

研究成果: ジャーナルへの寄稿学術誌査読

7 被引用数 (Scopus)

抄録

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.

本文言語英語
論文番号16
ジャーナルJournal of Scientific Computing
83
1
DOI
出版ステータス出版済み - 4月 1 2020

!!!All Science Journal Classification (ASJC) codes

  • ソフトウェア
  • 理論的コンピュータサイエンス
  • 数値解析
  • 工学(全般)
  • 計算理論と計算数学
  • 計算数学
  • 応用数学

フィンガープリント

「A Linearized Finite Difference Scheme for the Richards Equation Under Variable-Flux Boundary Conditions」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル