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Mathematical Problems in Engineering
Volume 2011, Article ID 178491, 17 pages
http://dx.doi.org/10.1155/2011/178491
Research Article

Modified Predictor-Corrector WAF Method for the Shallow Water Equations with Source Terms

1Department of Mathematics, Faculty of Sciences, Kasetsart University, Bangkok 10900, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

Received 5 January 2011; Revised 18 March 2011; Accepted 17 April 2011

Academic Editor: Dane Quinn

Copyright © 2011 Montri Maleewong. 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

A modified predictor-corrector scheme combining with the depth gradient method (DGM) and the weighted average flux (WAF) method has been presented to solve the one-dimensional shallow water equations with source terms. Approximate solutions in the predictor step are obtained by the DGM with piecewise-linear reconstructions in each cell volume. The source terms can then be calculated directly by these predicted values at the corresponding half-time step. In the corrector step, the TVD version of the WAF method is applied to calculate the numerical fluxes at the same half-time step for each cell face. The accuracy of numerical solutions is shown by applying the method to solve various test cases in both steady and unsteady problems with and without source terms. It shows that the numerical results are in good agreement with the existing analytical solutions as well as experimental data in some test cases.