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Finite element analysis of compressible and incompressible fluid-solid systems

Authors: Alfredo Bermúdez, Ricardo Durán and Rodolfo Rodríguez
Journal: Math. Comp. 67 (1998), 111-136
MSC (1991): Primary 65N25, 65N30; Secondary 70J30, 73K70, 76Q05
MathSciNet review: 1434937
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Abstract: This paper deals with a finite element method to solve interior fluid-structure vibration problems valid for compressible and incompressible fluids. It is based on a displacement formulation for both the fluid and the solid. The pressure of the fluid is also used as a variable for the theoretical analysis yielding a well posed mixed linear eigenvalue problem. Lowest order triangular Raviart-Thomas elements are used for the fluid and classical piecewise linear elements for the solid. Transmission conditions at the fluid-solid interface are taken into account in a weak sense yielding a nonconforming discretization. The method does not present spurious or circulation modes for nonzero frequencies. Convergence is proved and error estimates independent of the acoustic speed are given. For incompressible fluids, a convenient equivalent stream function formulation and a post-process to compute the pressure are introduced.

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Additional Information

Alfredo Bermúdez
Affiliation: Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain

Ricardo Durán
Affiliation: Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 – Buenos Aires, Argentina
ORCID: 0000-0003-1349-3708

Rodolfo Rodríguez
Affiliation: Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 4009, Concepción, Chile

Received by editor(s): March 6, 1995
Received by editor(s) in revised form: May 22, 1996
Article copyright: © Copyright 1998 American Mathematical Society