Finite element method to fluid-solid interaction problems with unbounded periodic interfaces

Consider a time‐harmonic acoustic plane wave incident onto a doubly periodic (biperiodic) surface from above. The medium above the surface is supposed to be filled with a homogeneous compressible inviscid fluid of constant mass density, whereas the region below is occupied by an isotropic and linear...

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Vydané v:Numerical methods for partial differential equations Ročník 32; číslo 1; s. 5 - 35
Hlavní autori: Hu, Guanghui, Rathsfeld, Andreas, Yin, Tao
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Blackwell Publishing Ltd 01.01.2016
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Predmet:
Acoustics
Constants
Convergence
convergence analysis
Density
Finite element method
fluid-solid interaction
Fluid-solid interactions
Helmholtz equation
Lamé system
Mathematical analysis
Mathematical models
periodic structure
Rayleigh expansion
variational approach
ISSN:0749-159X, 1098-2426
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Shrnutí:Consider a time‐harmonic acoustic plane wave incident onto a doubly periodic (biperiodic) surface from above. The medium above the surface is supposed to be filled with a homogeneous compressible inviscid fluid of constant mass density, whereas the region below is occupied by an isotropic and linearly elastic solid body characterized by its Lamé constants. This article is concerned with a variational approach to the fluid–solid interaction problems with unbounded biperiodic Lipschitz interfaces between the domains of the acoustic and elastic waves. The existence of quasiperiodic solutions in Sobolev spaces is established at arbitrary frequency of incidence, while uniqueness is proved only for small frequencies or for all frequencies excluding a discrete set. A finite element scheme coupled with Dirichlet‐to‐Neumann mappings is proposed and the convergence analysis is performed. The Dirichlet‐to‐Neumann mappings are approximated by truncated Rayleigh series expansions. Finally, numerical tests in 2D are presented to confirm the convergence of solutions and the energy balance formula. In particular, the frequency spectrum of normally reflected signals is plotted for water–brass and water–brass–water interfaces. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 5–35, 2016
Bibliografia:istex:5BE64C0674E38C09B37AB3EC015B5ABBB54CFAB0
ark:/67375/WNG-T7S2LHQT-3
ArticleID:NUM21980
China Scholarship Council and the NSFC Grant - No. 11371385; No. 11201506
German Research Foundation (DFG) - No. HU 2111/1-2
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:0749-159X
1098-2426
DOI:10.1002/num.21980