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Mathematical Problems in Engineering
Volume 2013, Article ID 672936, 7 pages
http://dx.doi.org/10.1155/2013/672936
Research Article

Numerical Solution of Advection-Diffusion Equation Using a Sixth-Order Compact Finite Difference Method

1Department of Civil Engineering, Faculty of Engineering, Pamukkale University, 20070 Denizli, Turkey
2Department of Mathematics, Faculty of Art and Science, Pamukkale University, 20070 Denizli, Turkey

Received 15 February 2013; Accepted 25 March 2013

Academic Editor: Guohe Huang

Copyright © 2013 Gurhan Gurarslan et al. 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.

Abstract

This study aims to produce numerical solutions of one-dimensional advection-diffusion equation using a sixth-order compact difference scheme in space and a fourth-order Runge-Kutta scheme in time. The suggested scheme here has been seen to be very accurate and a relatively flexible solution approach in solving the contaminant transport equation for . For the solution of the present equation, the combined technique has been used instead of conventional solution techniques. The accuracy and validity of the numerical model are verified through the presented results and the literature. The computed results showed that the use of the current method in the simulation is very applicable for the solution of the advection-diffusion equation. The present technique is seen to be a very reliable alternative to existing techniques for these kinds of applications.