The Technique of MIEELDLD in Computational Aeroacoustics

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-ordermethodswith 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.