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Calculation of low Mach number acoustics: a comparison of MPV, EIF and linearized Euler equations

Published online by Cambridge University Press:  15 June 2005

Sabine Roller ,
Thomas Schwartzkopff ,
Roland Fortenbach ,
Michael Dumbser  and
Claus-Dieter Munz
Sabine Roller
Affiliation:
High Performance Computing Center Stuttgart (HLRS), University of Stuttgart, Germany. roller@hlrs.de
Thomas Schwartzkopff
Affiliation:
Institute for Aerodynamics and Gasdynamics (IAG), University of Stuttgart, Germany. schwartzkopff@iag.uni-stuttgart.de
Roland Fortenbach
Affiliation:
Institute for Aerodynamics and Gasdynamics (IAG), University of Stuttgart, Germany. schwartzkopff@iag.uni-stuttgart.de
Michael Dumbser
Affiliation:
Institute for Aerodynamics and Gasdynamics (IAG), University of Stuttgart, Germany. schwartzkopff@iag.uni-stuttgart.de
Claus-Dieter Munz
Affiliation:
Institute for Aerodynamics and Gasdynamics (IAG), University of Stuttgart, Germany. schwartzkopff@iag.uni-stuttgart.de
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Abstract

The calculation of sound generation and propagation in low Mach number flows requires serious reflections on the characteristics of the underlying equations. Although the compressible Euler/Navier-Stokes equations cover all effects, an approximation via standard compressible solvers does not have the ability to represent acoustic waves correctly. Therefore, different methods have been developed to deal with the problem. In this paper, three of them are considered and compared to each other. They are the Multiple Pressure Variables Approach (MPV), the Expansion about Incompressible Flow (EIF) and a coupling method via heterogeneous domain decomposition. In the latter approach, the non-linear Euler equations are used in a domain as small as possible to cover the sound generation, and the locally linearized Euler equations approximated with a high-order scheme are used in a second domain to deal with the sound propagation. Comparisons will be given in construction principles as well as implementational effort and computational costs on actual numerical examples.

Keywords

Aero-acousticslow Mach number flowsasymptotic expansionheterogeneous domain decomposition.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 3: Special issue on Low Mach Number Flows Conference , May 2005 , pp. 561 - 576
Copyright
© EDP Sciences, SMAI, 2005

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