Discrete models for fluid-structure interactions: the Finite Element Immersed Boundary Method

TL;DR

This paper surveys the finite element Immersed Boundary Method (FE-IBM) for fluid-structure interactions, emphasizing the advantages of the distributed Lagrange multiplier formulation developed over the past decade.

Contribution

It provides a comprehensive overview of FE-IBM formulations, highlighting the novel DLM-IBM approach and its benefits over traditional methods.

Findings

DLM-IBM offers improved stability and accuracy.

The survey consolidates a decade of research developments.

Advantages of the DLM-IBM over original FE-IBM are demonstrated.

Abstract

The aim of this paper is to provide a survey of the state of the art in the finite element approach to the Immersed Boundary Method (FE-IBM) which has been investigated by the authors during the last decade. In a unified setting, we present the different formulation proposed in our research and highlight the advantages of the one based on a distributed Lagrange multiplier (DLM-IBM) over the original FE-IBM.