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
DOI:
https://doi.org/10.1090/S0025-5718-98-00901-6
MathSciNet review:
1434937
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Abstract | References | Similar Articles | Additional Information
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
Email:
bermudez@zmat.usc.es
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
Email:
rduran@mate.dm.uba.ar
Rodolfo Rodríguez
Affiliation:
Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 4009, Concepción, Chile
Email:
rodolfo@gauss.cfm.udec.cl
Received by editor(s):
March 6, 1995
Received by editor(s) in revised form:
May 22, 1996
Article copyright:
© Copyright 1998
American Mathematical Society