# 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

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topRoller, 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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- T. Schwartzkopff and C.-D. Munz, Direct simulation of aeroacoustics, in Proc. Applied Mathematics and Mechanics (GAMM 2002)2 (2002).
- T. Schwartzkopff and C.-D. Munz, Direct simulation of aeroacoustics, in Analysis and Simulation of Multifield Problems, W. Wendland and M. Efendiev, Eds., Springer. Lect. Notes Appl. Comput. Mech.12 (2003) 337–342.
- 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).
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- 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).
- 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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