Interaction of Acoustic Waves with Boundary

Part of the Advances in Mathematical Fluid Mechanics book series (AMFM)


As we have seen in the previous chapters, 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 the acoustic waves. If the physical domain is bounded, the acoustic waves, being reflected by the boundary, inevitably develop high frequency oscillations resulting in the weak convergence of the velocity field. This rather unpleasant phenomenon creates additional problems when handling the convective term in the momentum equation (cf. Sections 5.4.7, 6.6.3 above). In this chapter, we focus on the mechanisms so-far neglected by which the acoustic energy is dissipated into heat, and the ways in which the dissipation may be used in order to show strong (pointwise) convergence of the velocity.


Acoustic Wave Eigenvalue Problem Strong Convergence Singular Limit Homogeneous Dirichlet Boundary Condition 
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© Birkhäuser Verlag 2009

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