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Fluid Flow Modeling Read chapter Read first chapter

2017 | OriginalPaper | Chapter

7. Interaction of Acoustic Waves with Boundary

Authors : Eduard Feireisl, Antonín Novotný

Published in: Singular Limits in Thermodynamics of Viscous Fluids

Publisher: Springer International Publishing

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Abstract

One of the most delicate issues in the analysis of singular limits for the Navier-Stokes-Fourier system in the low Mach number regime is the influence of acoustic waves. If the physical domain is bounded and the complete slip boundary conditions imposed, the acoustic waves, being reflected by the boundary, inevitably develop high frequency oscillations resulting in the weak convergence of the velocity field, in particular, its gradient part converges to zero only in the sense of integral means. This rather unpleasant phenomenon creates additional problems when handling the convective term in the momentum equation. Here, we focus on the mechanisms by which the acoustic energy may be dissipated, and the ways how the dissipation may be used in order to show strong (pointwise) convergence of the velocities in the incompressible limit.

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Metadata
Title
Interaction of Acoustic Waves with Boundary
Authors
Eduard Feireisl
Antonín Novotný
Copyright Year
2017
Book
Singular Limits in Thermodynamics of Viscous Fluids

Print ISBN: 978-3-319-63780-8

Electronic ISBN: 978-3-319-63781-5

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-63781-5_7

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