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

Published online by Cambridge University Press:  15 June 2005

Sabine Roller ,
Thomas Schwartzkopff ,
Roland Fortenbach ,
Michael Dumbser  and
Claus-Dieter Munz
Sabine Roller
Affiliation:
High Performance Computing Center Stuttgart (HLRS), University of Stuttgart, Germany. roller@hlrs.de
Thomas Schwartzkopff
Affiliation:
Institute for Aerodynamics and Gasdynamics (IAG), University of Stuttgart, Germany. schwartzkopff@iag.uni-stuttgart.de
Roland Fortenbach
Affiliation:
Institute for Aerodynamics and Gasdynamics (IAG), University of Stuttgart, Germany. schwartzkopff@iag.uni-stuttgart.de
Michael Dumbser
Affiliation:
Institute for Aerodynamics and Gasdynamics (IAG), University of Stuttgart, Germany. schwartzkopff@iag.uni-stuttgart.de
Claus-Dieter Munz
Affiliation:
Institute for Aerodynamics and Gasdynamics (IAG), University of Stuttgart, Germany. schwartzkopff@iag.uni-stuttgart.de
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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.

Keywords

Aero-acousticslow Mach number flowsasymptotic expansionheterogeneous domain decomposition.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 3: Special issue on Low Mach Number Flows Conference , May 2005 , pp. 561 - 576
Copyright
© EDP Sciences, SMAI, 2005

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References

M. Dumbser and C.-D. Munz, Arbitrary High Order Discontinuous Galerkin Schemes. IRMA series in mathematics and theoretical physics.
R. Fortenbach and C.-D. Munz, Multiple Scale considerations for sound generation in low Mach number flow, in Proc. The GAMM Jahrestagung, Augsburg, Germany, March 25–28 (2002).
K. Geratz, Erweiterung eines Godunov-Typ-Verfahrens für zwei-dimensionale kompressible Strömungen auf die Fälle kleiner und verschwindender Machzahl. Ph.D. Thesis, RWTH Aachen (1997).
Hardin, J. and Pope, D., An acoustic/viscous splitting technique for computational aeroacoustics. Theoret. Comput. Fluid Dynamics 6 (1994) 323–340. CrossRef
Klainerman, S. and Majda, A., Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible Limit of Compressible Fluids. Comm. Pure Appl. Math. 34 (1981) 481–524. CrossRef
Klein, R., 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. CrossRef
Klein, R., Botta, N., Hofmann, L., Meister, A., Munz, C.-D., Roller, S. and Sonar, T., Asymptotic adaptive methods for multiscale problems in fluid mechanics. J. Engrg. Math. 39 (2001) 261–343. CrossRef
Meister, A., Asymptotic single and multiple scale expansions in the mow Mach number limit. SIAM J. Appl. Math. 60 (1999) 256–271. CrossRef
Mitchell, B.E., Lele, S.K. and Moin, P., Direct computation of the sound from a compressible co-rotating vortex pair. J. Fluid Mech. 285 (1995) 181–202. CrossRef
Munz, C.-D., Roller, S., Klein, R. and Geratz, K.J., The extension of incompressible flow solvers to the weakly compressible regime. Comput. Fluids 32 (2003) 173–196. CrossRef
S. Roller, Ein numerisches verfahren zur simulation schwach kompressibler Strömungen. Ph.D. Thesis, University of Stuttgart (2004).
Roller, S. and Munz, C.-D., A low Mach number scheme based on multi-scale asymptotics. Comput. Visual. Sci. 3 (2000) 85–91. CrossRef
Schneider, T., Botta, N., Geratz, K. and Klein, R., Extension of finite volume compressible flow solvers to multi-dimensional, variable density zero Mach number flow. J. Comput. Phys. 155 (1999) 248–286. CrossRef
T. Schwartzkopff, Finite-Volumen Verfahren hoher Ordnung und heterogene Gebietszerlegung für die numerische Aeroakustik. Ph.D. Thesis, University of Stuttgart (2005).
T. Schwartzkopff and C.-D. Munz, Direct simulation of aeroacoustics, in Proc. Applied Mathematics and Mechanics (GAMM 2002) 2 (2002).
Schwartzkopff, T. and Munz, C.-D., 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. CrossRef
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).
Schwartzkopff, T., Dumbser, M. and Munz, C.-D., Fast high order ADER schemes for linear hyperbolic equations. J. Comput. Phys. 197 (2004) 532–539. CrossRef
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).