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.
Mots clés : 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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {561--576},
publisher = {EDP-Sciences},
volume = {39},
number = {3},
year = {2005},
doi = {10.1051/m2an:2005016},
mrnumber = {2157150},
zbl = {1130.76072},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an:2005016/}
}
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: Modélisation mathématique et analyse numérique PY - 2005 SP - 561 EP - 576 VL - 39 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2005016/ DO - 10.1051/m2an:2005016 LA - en ID - M2AN_2005__39_3_561_0 ER -
%0 Journal Article %A Roller, Sabine %A Schwartzkopff, Thomas %A Fortenbach, Roland %A Dumbser, Michael %A Munz, Claus-Dieter %T Calculation of low Mach number acoustics : a comparison of MPV, EIF and linearized Euler equations %J ESAIM: Modélisation mathématique et analyse numérique %D 2005 %P 561-576 %V 39 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2005016/ %R 10.1051/m2an:2005016 %G en %F 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: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 3, pp. 561-576. doi : 10.1051/m2an:2005016. http://archive.numdam.org/articles/10.1051/m2an:2005016/
[1] and, Arbitrary High Order Discontinuous Galerkin Schemes. IRMA series in mathematics and theoretical physics. | MR
[2] and, Multiple Scale considerations for sound generation in low Mach number flow, in Proc. The GAMM Jahrestagung, Augsburg, Germany, March 25-28 (2002).
[3] , Erweiterung eines Godunov-Typ-Verfahrens für zwei-dimensionale kompressible Strömungen auf die Fälle kleiner und verschwindender Machzahl. Ph.D. Thesis, RWTH Aachen (1997).
[4] and, An acoustic/viscous splitting technique for computational aeroacoustics. Theoret. Comput. Fluid Dynamics 6 (1994) 323-340. | Zbl
[5] and, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible Limit of Compressible Fluids. Comm. Pure Appl. Math. 34 (1981) 481-524. | Zbl
[6] , Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics I: One dimensional flow. J. Comput. Phys. 121 (1995) 213-237. | Zbl
[7] ,,,,, and, Asymptotic adaptive methods for multiscale problems in fluid mechanics. J. Engrg. Math. 39 (2001) 261-343. | Zbl
[8] , Asymptotic single and multiple scale expansions in the mow Mach number limit. SIAM J. Appl. Math. 60 (1999) 256-271. | Zbl
[9] , and, Direct computation of the sound from a compressible co-rotating vortex pair. J. Fluid Mech. 285 (1995) 181-202. | Zbl
[10] ,, and, The extension of incompressible flow solvers to the weakly compressible regime. Comput. Fluids 32 (2003) 173-196. | Zbl
[11] , Ein numerisches verfahren zur simulation schwach kompressibler Strömungen. Ph.D. Thesis, University of Stuttgart (2004).
[12] and, A low Mach number scheme based on multi-scale asymptotics. Comput. Visual. Sci. 3 (2000) 85-91. | Zbl
[13] ,, and, Extension of finite volume compressible flow solvers to multi-dimensional, variable density zero Mach number flow. J. Comput. Phys. 155 (1999) 248-286. | Zbl
[14] , Finite-Volumen Verfahren hoher Ordnung und heterogene Gebietszerlegung für die numerische Aeroakustik. Ph.D. Thesis, University of Stuttgart (2005).
[15] and, Direct simulation of aeroacoustics, in Proc. Applied Mathematics and Mechanics (GAMM 2002) 2 (2002).
[16] and, 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.
[17] , and, CAA using domain decomposition and high order methods on structured and unstructured meshes, in 10th AIAA/CEAS Aeroacoustic Conference, Manchester, GB (2004).
[18] , and, Fast high order ADER schemes for linear hyperbolic equations. J. Comput. Phys. 197 (2004) 532-539. | Zbl
[19] ,, and, ADER-2d: A very high-order approach for linear hyperbolic systems, in Proceedings of ECCOMAS CFD Conference 2001 (September 2001). | Zbl
[20] and, ADER: High-order non-oscillatory advection schemes, in Proceedings of the 8th International Conference on Nonlinear Hyperbolic Problems, preprint (February 2000).
Cité par Sources :
