Journal of Applied Mathematics
Volume 2013 (2013), Article ID 428681, 12 pages
http://dx.doi.org/10.1155/2013/428681
Research Article

Optimized Weighted Essentially Nonoscillatory Third-Order Schemes for Hyperbolic Conservation Laws

A. R. Appadu1 and A. A. I. Peer2

1Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa
2Department of Applied Mathematical Sciences, University of Technology, Mauritius, La Tour Koenig, Pointe-aux-Sables, Mauritius

Received 12 April 2013; Revised 25 June 2013; Accepted 25 June 2013

Academic Editor: Mohamed Fathy El-Amin

Copyright © 2013 A. R. Appadu and A. A. I. Peer. 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

We describe briefly how a third-order Weighted Essentially Nonoscillatory (WENO) scheme is derived by coupling a WENO spatial discretization scheme with a temporal integration scheme. The scheme is termed WENO3. We perform a spectral analysis of its dispersive and dissipative properties when used to approximate the 1D linear advection equation and use a technique of optimisation to find the optimal cfl number of the scheme. We carry out some numerical experiments dealing with wave propagation based on the 1D linear advection and 1D Burger’s equation at some different cfl numbers and show that the optimal cfl does indeed cause less dispersion, less dissipation, and lower errors. Lastly, we test numerically the order of convergence of the WENO3 scheme.