A time–dependent FEM-BEM coupling method for fluid–structure interaction in 3d

Heiko Gimperlein, Ceyhun Özdemir, Ernst P. Stephan

Research output: Contribution to journalArticle

Abstract

We consider the well-posedness and a priori error estimates of a 3d FEM-BEM coupling method for fluid-structure interaction in the time domain. For an elastic body immersed in a fluid, the exterior linear wave equation for the fluid is reduced to an integral equation on the boundary involving the Poincaré-Steklov operator. The resulting problem is solved using a Galerkin boundary element method in the time domain, coupled to a finite element method for the Lamé equation inside the elastic body. Based on ideas from the time–independent coupling formulation, we obtain an a priori error estimate and discuss the implementation of the proposed method. Numerical experiments illustrate the performance of our scheme for model problems.
Original languageEnglish
Pages (from-to)49-65
Number of pages17
JournalApplied Numerical Mathematics
Volume152
Early online date4 Feb 2020
DOIs
Publication statusE-pub ahead of print - 4 Feb 2020

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Coupling Method
A Priori Error Estimates
Elastic body
Fluid
Time Domain
Interaction
Well-posedness
Galerkin
Boundary Elements
Wave equation
Linear equation
Integral Equations
Finite Element Method
Numerical Experiment
Formulation
Operator
Model

Cite this

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title = "A time–dependent FEM-BEM coupling method for fluid–structure interaction in 3d",
abstract = "We consider the well-posedness and a priori error estimates of a 3d FEM-BEM coupling method for fluid-structure interaction in the time domain. For an elastic body immersed in a fluid, the exterior linear wave equation for the fluid is reduced to an integral equation on the boundary involving the Poincar{\'e}-Steklov operator. The resulting problem is solved using a Galerkin boundary element method in the time domain, coupled to a finite element method for the Lam{\'e} equation inside the elastic body. Based on ideas from the time–independent coupling formulation, we obtain an a priori error estimate and discuss the implementation of the proposed method. Numerical experiments illustrate the performance of our scheme for model problems.",
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A time–dependent FEM-BEM coupling method for fluid–structure interaction in 3d. / Gimperlein, Heiko; Özdemir, Ceyhun; Stephan, Ernst P.

In: Applied Numerical Mathematics, Vol. 152, 06.2020, p. 49-65.

Research output: Contribution to journalArticle

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AU - Özdemir, Ceyhun

AU - Stephan, Ernst P.

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