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

Sabine Roller; Thomas Schwartzkopff; Roland Fortenbach; Michael Dumbser; Claus-Dieter Munz

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2005)

  • Volume: 39, Issue: 3, page 561-576
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Roller, Sabine, et al. "Calculation of low Mach number acoustics : a comparison of MPV, EIF and linearized Euler equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 39.3 (2005): 561-576. <http://eudml.org/doc/246015>.

@article{Roller2005,
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.},
author = {Roller, Sabine, Schwartzkopff, Thomas, Fortenbach, Roland, Dumbser, Michael, Munz, Claus-Dieter},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {aero-acoustics; low Mach number flows; asymptotic expansion; heterogeneous domain decomposition},
language = {eng},
number = {3},
pages = {561-576},
publisher = {EDP-Sciences},
title = {Calculation of low Mach number acoustics : a comparison of MPV, EIF and linearized Euler equations},
url = {http://eudml.org/doc/246015},
volume = {39},
year = {2005},
}

TY - JOUR
AU - Roller, Sabine
AU - Schwartzkopff, Thomas
AU - Fortenbach, Roland
AU - Dumbser, Michael
AU - Munz, Claus-Dieter
TI - Calculation of low Mach number acoustics : a comparison of MPV, EIF and linearized Euler equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2005
PB - EDP-Sciences
VL - 39
IS - 3
SP - 561
EP - 576
AB - 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.
LA - eng
KW - aero-acoustics; low Mach number flows; asymptotic expansion; heterogeneous domain decomposition
UR - http://eudml.org/doc/246015
ER -

References

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