Cite this article as:

Gerus . A., Gritsenko S. . Homogenization of the Acoustics Mathematical Model. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2015, vol. 15, iss. 3, pp. 264-272. DOI: https://doi.org/10.18500/1816-9791-2015-15-3-264-272

Language: 
Russian
Heading: 
Mathematics
UDC: 
517.958

Homogenization of the Acoustics Mathematical Model

Authors: 
Gerus Artur Andreevich, Belgorod State National Research University, 85, Pobedy st., 308015, Belgorod, Russia , artur-gerus@bsu.edu.ru
Gritsenko Svetlana Aleksandrovna, Belgorod State National Research University, 85, Pobedy st., 308015, Belgorod, Russia , sgritsenko@bsu.edu.ru
Abstract: 

We consider a mathematical model of acoustics in heterogeneous medium with two different components with the common boundary. One of these is a bounded liquid domain and the other is a poroelastic medium. Poroelastic medium is perforated by pores. A pore space is filled with a viscous liquid. The motion of the liquid and the joint motion of the poroelastic media with porous space are governed by the differential equations based on the continuum mechanics laws. These equations contain rapidly oscillating terms, depending on the small parameter. The small parameter is the ratio of the average pores size to the size of domain under consideration. Rapidly oscillating terms prevent from the numerical simulations. The unique existence of the generalized solution of the boundary-value problem is proved. Homogenized equations (i.e. free from rapidly oscillating terms) are based upon the Nguetseng method of the two-scale convergence. We derived approximate models useful to the numerical calculations.

Key words: 
composite medium, periodic structure, Stokes equations, Lame’s equations, acoustics equations, poroelastic, homogenization of periodic structures, two-scale convergence
DOI: 
https://doi.org/10.18500/1816-9791-2015-15-3-264-272
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