Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Gerus A. A., Gritsenko S. A. Homogenization of the Acoustics Mathematical Model. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2015, vol. 15, iss. 3, pp. 264-272. DOI: 10.18500/1816-9791-2015-15-3-264-272, EDN: UKIVEB

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
11.09.2015
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Russian
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UDC: 
517.958
EDN: 
UKIVEB

Homogenization of the Acoustics Mathematical Model

Autors: 
Gerus Artur Andreevich, Federal State Autonomous Educational Institution of Higher Education ”Belgorod State University”
Gritsenko Svetlana Aleksandrovna, Federal State Autonomous Educational Institution of Higher Education ”Belgorod State University”
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.

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Received: 
11.04.2015
Accepted: 
27.08.2015
Published: 
30.09.2015