Journal of Applied Mathematics
Volume 2012 (2012), Article ID 783101, 30 pages
Research Article

The Technique of MIEELDLD in Computational Aeroacoustics

Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa

Received 3 January 2012; Accepted 14 February 2012

Academic Editor: M. F. El-Amin

Copyright © 2012 A. R. Appadu. 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.


The numerical simulation of aeroacoustic phenomena requires high-order accurate numerical schemes with low dispersion and low dissipation errors. A technique has recently been devised in a Computational Fluid Dynamics framework which enables optimal parameters to be chosen so as to better control the grade and balance of dispersion and dissipation in numerical schemes (Appadu and Dauhoo, 2011; Appadu, 2012a; Appadu, 2012b; Appadu, 2012c). This technique has been baptised as the Minimized Integrated Exponential Error for Low Dispersion and Low Dissipation (MIEELDLD) and has successfully been applied to numerical schemes discretising the 1-D, 2-D, and 3-D advection equations. In this paper, we extend the technique of MIEELDLD to the field of computational aeroacoustics and have been able to construct high-order methods with Low Dispersion and Low Dissipation properties which approximate the 1-D linear advection equation. Modifications to the spatial discretization schemes designed by Tam and Webb (1993), Lockard et al. (1995), Zingg et al. (1996), Zhuang and Chen (2002), and Bogey and Bailly (2004) have been obtained, and also a modification to the temporal scheme developed by Tam et al. (1993) has been obtained. These novel methods obtained using MIEELDLD have in general better dispersive properties as compared to the existing optimised methods.