Error analysis of finite difference methods for two-dimensional advection-dispersion-reaction equation

B. Ataie-Ashtiani, S. A. Hosseini

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)


In this paper, the numerical errors associated with the finite difference solutions of two-dimensional advection-dispersion equation with linear sorption are obtained from a Taylor analysis and are removed from numerical solution. The error expressions are based on a general form of the corresponding difference equation. The variation of these numerical truncation errors is presented as a function of Peclet and Courant numbers in X and Y direction, a Sink/Source dimensionless number and new form of Peclet and Courant numbers in X-Y plane. It is shown that the Crank-Nicolson method is the most accurate scheme based on the truncation error analysis. The effects of these truncation errors on the numerical solution of a two-dimensional advection-dispersion equation with a first-order reaction or degradation are demonstrated by comparison with an analytical solution for predicting contaminant plume distribution in uniform flow field. Considering computational efficiency, an alternating direction implicit method is used for the numerical solution of governing equation. The results show that removing these errors improves numerical result and reduces differences between numerical and analytical solution.

Original languageEnglish
Pages (from-to)793-806
Number of pages14
JournalAdvances in Water Resources
Issue number8
Publication statusPublished - Aug 2005
Externally publishedYes


  • Advection-dispersion-reaction equation
  • Finite difference method
  • Numerical method
  • Truncation errors


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