A distributed Lagrange formulation of the Finite Element Immersed Boundary Method for fluids interacting with compressible solids

TL;DR

This paper introduces a distributed Lagrange multiplier approach to the Finite Element Immersed Boundary Method, enabling stable coupling of incompressible fluids with compressible solids through a cleaner variational formulation.

Contribution

It generalizes previous formulations by incorporating distributed Lagrange multipliers, improving the separation and stability of fluid-solid interaction modeling.

Findings

Provides a stable variational formulation

Offers preliminary numerical validation

Enhances fluid-solid coupling accuracy

Abstract

We present a distributed Lagrange multiplier formulation of the Finite Element Immersed Boundary Method to couple incompressible fluids with compressible solids. This is a generalization of the formulation presented in Heltai and Costanzo (2012), that offers a cleaner variational formulation, thanks to the introduction of distributed Lagrange multipliers, that acts as intermediary between the fluid and solid equations, keeping the two formulation mostly separated. Stability estimates and a brief numerical validation are presented.