Modified immersed finite element method for fully-coupled fluid–structure interactions

Abstract

In this paper, we develop a “modified” immersed finite element method (mIFEM), a non-boundary-fitted numerical technique, to study fluid-structure interactions. Using this method, we can more precisely capture the solid dynamics by solving the solid governing equation instead of imposing it based on the fluid velocity field as in the original immersed finite element (IFEM). Using the IFEM may lead to severe solid mesh distortion because the solid deformation is been over-estimated, especially for high Reynolds number flows. In the mIFEM, the solid dynamics is solved using appropriate boundary conditions generated from the surrounding fluid, therefore produces more accurate and realistic coupled solutions. We show several 2-D and 3-D testing cases where the mIFEM has a noticeable advantage in handling complicated fluid-structure interactions when the solid behavior dominates the fluid flow.

Fully-coupled aeroelastic simulation with fluid compressibility — For application to vocal fold vibration

“…The mIFEM addresses these problems by re-formulating the coupling scheme and solving for the solid dynamics rather than imposing it. A more detailed derivation of the algorithm can be found in [14]. It has been rigorously derived and verified with 2-D and 3-D studies [24,14,25,26].…”

“…It is built based on a fully-coupled fluid–structure interaction algorithm, the modified immersed finite element method (mIFEM) [14]. The major distinction between the class of immersed finite element methods and that of the IB methods is that it utilizes the concept of principle of virtual work to remove the artificial effects from the overlapping background fluid, thus providing an independent and accurate solid material description.…”

Modeling of coupled dynamics for fluid-structure interactions

“…However, in high Reynolds number flows, letting the solid follow the fluid movement may lead to unrealistic solid deformation and sometimes even causes the distortion of the solid mesh, because the solid deformation may be over-estimated following high fluid velocities. A modified IFEM algorithm (mIFEM) 42 In this paper, we focus in particular the detail derivation and descriptions of the mathematical formulations for IFEM, the semi-implicit IFEM, and eventually the modified IFEM. For each of the improvements made from the IFEM algorithm, the readers can clearly identify the rationale behind them, as well as understanding the necessity of incorporating the dynamics into the coupled systems.…”

A one-field monolithic fictitious domain method for fluid–structure interactions

“…On an unfitted mesh, there is no clear boundary for the solid problem, so it is not easy to enforce the boundary condition and solve the solid equation. A wide variety of schemes have been proposed to address this issue, including the Immersed Finite Element Method (IFEM) [9,10,11,12,13] and the Fictitious Domain method (FDM) [14,15,16,17,18]. The IFEM de-40 veloped from the Immersed Boundary method first introduced by Peskin [19], and has had great success with applications in bioscience and biomedical fields.…”

“…Instead, the solid equations are arranged on the right-hand side of the fluid equations as an FSI force, and these modified fluid equations are solved on the augmented domain 45 (occupied by fluid and solid). There is also the Modified IFEM [13], which solves the solid equations explicitly and iterates until convergence. The FDM has a similar spirit to IFEM in that it treats the domain occupied by solid as a fictitious/artificial fluid whose velocity/displacement is constrained to be the same as that of the solid.…”