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Journal of Applied Mathematics
Volume 2014, Article ID 396738, 8 pages
Research Article

Accurate Simulation of Contaminant Transport Using High-Order Compact Finite Difference Schemes

Department of Civil Engineering, Faculty of Engineering, Pamukkale University, 20070 Pamukkale, Denizli, Turkey

Received 24 January 2014; Revised 27 March 2014; Accepted 10 April 2014; Published 29 April 2014

Academic Editor: Yuefei Huang

Copyright © 2014 Gurhan Gurarslan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Numerical simulation of advective-dispersive contaminant transport is carried out by using high-order compact finite difference schemes combined with second-order MacCormack and fourth-order Runge-Kutta schemes. Both of the two schemes have accuracy of sixth-order in space. A sixth-order MacCormack scheme is proposed for the first time within this study. For the aim of demonstrating efficiency and high-order accuracy of the current methods, some numerical experiments have been done. The schemes are implemented to solve two test problems with known exact solutions. It has been exhibited that the methods are capable of succeeding high accuracy and efficiency with minimal computational effort, by comparisons of the computed results with exact solutions.