Published 6 issues per year
ISSN Print: 1543-1649
ISSN Online: 1940-4352
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Acoustic Wave Propagation in a Composite of Two Different Poroelastic Materials with a Very Rough Periodic Interface: a Homogenization Approach
ABSTRACT
Homogenization is used to analyze the system of Biot-type partial differential equations in a domain of two different poroelastic materials with a very rough periodic interface. It is shown that by using homogenization, such a rough interface can be replaced by an equivalent flat layer within which a system of modified differential equations holds. The coefficients of this new system of equations are certain "effective" parameters. These coefficients are determined by solutions of the auxiliary problems which involve the detailed structure of the interface. In this paper, the auxiliary problems are derived and the homogenized system of equations is given.
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Lemoine Grady I., Ou M. Yvonne, LeVeque Randall J., High-Resolution Finite Volume Modeling of Wave Propagation in Orthotropic Poroelastic Media, SIAM Journal on Scientific Computing, 35, 1, 2013. Crossref
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Yvonne Ou Miao-Jung, On reconstruction of dynamic permeability and tortuosity from data at distinct frequencies, Inverse Problems, 30, 9, 2014. Crossref
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Lemoine Grady I., Ou M. Yvonne, Finite Volume Modeling of Poroelastic-Fluid Wave Propagation with Mapped Grids, SIAM Journal on Scientific Computing, 36, 3, 2014. Crossref
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