Linearized acoustic perturbation equations for low Mach number flow with variable density and temperature
Abstract
When the Mach number tends to zero the compressible NavierStokes equations converge to the incompressible NavierStokes equations, under the restrictions of constant density, constant temperature and no compression from the boundary. This is a singular limit in which the pressure of the compressible equations converges at leading order to a constant thermodynamic background pressure, while a hydrodynamic pressure term appears in the incompressible equations as a Lagrangian multiplier to establish the divergencefree condition for the velocity. In this paper we consider the more general case in which variable density, variable temperature and heat transfer are present, while the Mach number is small. We discuss first the limit equations for this case, when the Mach number tends to zero. The introduction of a pressure splitting into a thermodynamic and a hydrodynamic part allows the extension of numerical methods to the zero Mach number equations in these nonstandard situations. The solution of these equations is then used as the state of expansion extending the expansion about incompressible flow proposed by Hardin and Pope [J.C. Hardin, D.S. Pope, An acoustic/viscous splitting technique for computational aeroacoustics, Theor. Comput. Fluid Dyn. 6 (1995) 323340]. The resulting linearized equations state a mathematical model for the generationmore »
 Authors:
 University of Stuttgart, Institute of Aerodynamics and Gasdynamics, Pfaffenwaldring 21, 70550 Stuttgart (Germany). Email: clausdieter.munz@iag.unistuttgart.de
 University of Stuttgart, Institute of Aerodynamics and Gasdynamics, Pfaffenwaldring 21, 70550 Stuttgart (Germany). Email: michael.dumbser@iag.unistuttgart.de
 High Performance Computing Center Stuttgart (HLRS), Nobelstr. 19, 70550 Stuttgart (Germany). Email: roller@hlrs.de
 Publication Date:
 OSTI Identifier:
 20991583
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Computational Physics; Journal Volume: 224; Journal Issue: 1; Other Information: DOI: 10.1016/j.jcp.2007.02.022; PII: S00219991(07)00085X; Copyright (c) 2007 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPRESSION; EXPANSION; HEAT TRANSFER; INCOMPRESSIBLE FLOW; LAGRANGIAN FUNCTION; MACH NUMBER; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS; NAVIERSTOKES EQUATIONS; PERTURBATION THEORY; SOUND WAVES
Citation Formats
Munz, ClausDieter, Dumbser, Michael, and Roller, Sabine. Linearized acoustic perturbation equations for low Mach number flow with variable density and temperature. United States: N. p., 2007.
Web. doi:10.1016/j.jcp.2007.02.022.
Munz, ClausDieter, Dumbser, Michael, & Roller, Sabine. Linearized acoustic perturbation equations for low Mach number flow with variable density and temperature. United States. doi:10.1016/j.jcp.2007.02.022.
Munz, ClausDieter, Dumbser, Michael, and Roller, Sabine. Sun .
"Linearized acoustic perturbation equations for low Mach number flow with variable density and temperature". United States.
doi:10.1016/j.jcp.2007.02.022.
@article{osti_20991583,
title = {Linearized acoustic perturbation equations for low Mach number flow with variable density and temperature},
author = {Munz, ClausDieter and Dumbser, Michael and Roller, Sabine},
abstractNote = {When the Mach number tends to zero the compressible NavierStokes equations converge to the incompressible NavierStokes equations, under the restrictions of constant density, constant temperature and no compression from the boundary. This is a singular limit in which the pressure of the compressible equations converges at leading order to a constant thermodynamic background pressure, while a hydrodynamic pressure term appears in the incompressible equations as a Lagrangian multiplier to establish the divergencefree condition for the velocity. In this paper we consider the more general case in which variable density, variable temperature and heat transfer are present, while the Mach number is small. We discuss first the limit equations for this case, when the Mach number tends to zero. The introduction of a pressure splitting into a thermodynamic and a hydrodynamic part allows the extension of numerical methods to the zero Mach number equations in these nonstandard situations. The solution of these equations is then used as the state of expansion extending the expansion about incompressible flow proposed by Hardin and Pope [J.C. Hardin, D.S. Pope, An acoustic/viscous splitting technique for computational aeroacoustics, Theor. Comput. Fluid Dyn. 6 (1995) 323340]. The resulting linearized equations state a mathematical model for the generation and propagation of acoustic waves in this more general low Mach number regime and may be used within a hybrid aeroacoustic approach.},
doi = {10.1016/j.jcp.2007.02.022},
journal = {Journal of Computational Physics},
number = 1,
volume = 224,
place = {United States},
year = {Sun May 20 00:00:00 EDT 2007},
month = {Sun May 20 00:00:00 EDT 2007}
}

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