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A monolithic arbitrary Lagrangian–Eulerian‐based finite element strategy for fluid–structure interaction problems involving a compressible fluid

In this work, we present a new monolithic finite element strategy for solving fluid–structure interaction problems involving a compressible fluid and a hyperelastic structure. In the Lagrangian limit, the time‐stepping strategy that we propose conserves the total energy, and linear and angular momen...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2021-11, Vol.122 (21), p.6037-6102
Main Authors: Dutta, Suman, Jog, C. S.
Format: Article
Language:English
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Summary:In this work, we present a new monolithic finite element strategy for solving fluid–structure interaction problems involving a compressible fluid and a hyperelastic structure. In the Lagrangian limit, the time‐stepping strategy that we propose conserves the total energy, and linear and angular momenta. Detailed proofs with numerical validations are provided. We use a displacement‐based Lagrangian formulation for the structure, and a velocity‐based arbitrary Lagrangian–Eulerian mixed formulation with appropriately chosen interpolations for the various field variables to ensure stability of the resulting numerical procedure. A hybrid formulation is used to prevent locking of thin structures. Apart from physical variables such as displacement, velocity, and so forth, no new variables are introduced in the formulation. The use of the exact tangent stiffness matrix ensures that the algorithm converges quadratically within each time step. A number of benchmark examples have been solved to illustrate the good performance of the proposed method.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.6783