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 (2010)

  • 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 39.3 (2010): 561-576. <http://eudml.org/doc/194275>.

@article{Roller2010,
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},
keywords = {Aero-acoustics; low Mach number flows; asymptotic expansion; heterogeneous domain decomposition.},
language = {eng},
month = {3},
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/194275},
volume = {39},
year = {2010},
}

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
DA - 2010/3//
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/194275
ER -

References

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  17. T. Schwartzkopff, M. Dumbser and C.-D. Munz, CAA using domain decomposition and high order methods on structured and unstructured meshes, in 10th AIAA/CEAS Aeroacoustic Conference, Manchester, GB (2004).  
  18. T. Schwartzkopff, M. Dumbser and C.-D. Munz, Fast high order ADER schemes for linear hyperbolic equations. J. Comput. Phys.197 (2004) 532–539.  
  19. T. Schwartzkopff, C.-D. Munz, E. Toro and R. Millington, ADER-2d: A very high-order approach for linear hyperbolic systems, in Proceedings of ECCOMAS CFD Conference 2001 (September 2001).  
  20. E. Toro and R. Millington, ADER: High-order non-oscillatory advection schemes, in Proceedings of the 8th International Conference on Nonlinear Hyperbolic Problems, preprint (February 2000).  

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