The Technique of MIEELDLD in Computational Aeroacoustics

A R Appadu

doi:10.1155/2012/783101

Abstract

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.

Highlights

Computational aeroacoustics CAA has been given increased interest because of the need to better control noise levels from aircrafts, trains, and cars due to increased transport and stricter regulations from authorities 1
We extend the measures used by Tam and Webb 3, Bogey and Bailly 16, Berland et al 28 in a computational aeroacoustics framework to suit them in a computational fluid dynamics framework such that the optimal cfl of some known numerical methods can be obtained
We have used the technique of Minimised Integrated Exponential Error for Low Dispersion and Low Dissipation MIEELDLD in a computational aeroacoustics framework to obtain modifications to optimized spatial schemes constructed by Tam and Webb 3, Zingg et al 14, Lockard et al 13, Zhuang and Chen, and Bogey and Bailly, and a modification to the optimized temporal scheme devised by Tam et al is obtained

Summary

Introduction

Computational aeroacoustics CAA has been given increased interest because of the need to better control noise levels from aircrafts, trains, and cars due to increased transport and stricter regulations from authorities 1. The accurate prediction of the generation of sound is demanding due to the requirement for preservation of the shape and frequency of wave propagation and generation. It is well known 2, 3 that, in order to conduct satisfactory computational aeroacoustics, numerical methods must generate the least possible dispersion. Higher order schemes would be more suitable for CAA than the lower-order schemes since, overall, the former are less dissipative 4. This is the reason why higher-order spatial discretisation schemes have gained considerable interest in computational aeroacoustics

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Conclusion