# A monolithic arbitrary Lagrangianâ��Eulerian-based finite element strategy for fluidâ��structure interaction problems involving a compressible fluid

Dutta, S and Jog, CS (2021) A monolithic arbitrary Lagrangianâ��Eulerian-based finite element strategy for fluidâ��structure interaction problems involving a compressible fluid. In: International Journal for Numerical Methods in Engineering .

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Official URL: https://doi.org/10.1002/nme.6783

## Abstract

In this work, we present a new monolithic finite element strategy for solving fluidâ��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 Lagrangianâ��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. Â© 2021 John Wiley & Sons Ltd.

Item Type: Journal Article International Journal for Numerical Methods in Engineering John Wiley and Sons Ltd The copyright for this article belongs to John Wiley and Sons Ltd Benchmarking; Finite element method; Stiffness matrix, Compressible fluids; Hybrid formulations; Interaction problems; Lagrangian formulations; Numerical procedures; Numerical validations; Physical variables; Tangent stiffness matrix, Lagrange multipliers Division of Mechanical Sciences > Mechanical Engineering 03 Dec 2021 06:52 03 Dec 2021 06:52 http://eprints.iisc.ac.in/id/eprint/70109