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, Volume 39 (2005) no. 3, p. 561-576

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.

DOI : https://doi.org/10.1051/m2an:2005016
Classification:  41A60,  65M55,  76Q05
Keywords: aero-acoustics, low Mach number flows, asymptotic expansion, heterogeneous domain decomposition
@article{M2AN_2005__39_3_561_0,
     author = {Roller, Sabine and Schwartzkopff, Thomas and Fortenbach, Roland and Dumbser, Michael and Munz, Claus-Dieter},
     title = {Calculation of low Mach number acoustics : a comparison of MPV, EIF and linearized Euler equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {3},
     year = {2005},
     pages = {561-576},
     doi = {10.1051/m2an:2005016},
     zbl = {1130.76072},
     mrnumber = {2157150},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2005__39_3_561_0}
}
Roller, Sabine; Schwartzkopff, Thomas; Fortenbach, Roland; Dumbser, Michael; Munz, Claus-Dieter. 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, Volume 39 (2005) no. 3, pp. 561-576. doi : 10.1051/m2an:2005016. http://www.numdam.org/item/M2AN_2005__39_3_561_0/

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