Numerical errors of explicit finite difference approximation for two-dimensional solute transport equation with linear sorption

B. Ataie-Ashtiani, S. A. Hosseini

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

The numerical errors associated with explicit upstream finite difference solutions of two-dimensional advection - Dispersion equation with linear sorption are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation. The numerical truncation errors are defined using Peclet and Courant numbers in the X and Y direction, a sink/source dimensionless number and new Peclet and Courant numbers in the XY plane. The effects of these truncation errors on the explicit solution of a two-dimensional advection-dispersion equation with a first-order reaction or degradation are demonstrated by comparison with an analytical solution in uniform flow field. The results show that these errors are not negligible and correcting the finite difference scheme for them results in a more accurate solution.

Original languageEnglish
Pages (from-to)817-826
Number of pages10
JournalEnvironmental Modelling and Software
Volume20
Issue number7
DOIs
Publication statusPublished - Jul 2005
Externally publishedYes

Keywords

  • Advection - Dispersion-Reaction equation
  • Finite Difference Model
  • Numerical methods
  • Truncation errors

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