Immersed-Boundary Fluid-Structure Interaction of Membranes and Shells

TL;DR

This paper introduces a versatile and stable computational method combining immersed-boundary and finite-element techniques to simulate fluid-structure interactions involving large displacements and added-mass effects in membranes and shells.

Contribution

It develops a general, robust, and efficient partitioned solver with a strongly-coupled algorithm that avoids inverse Jacobian computations for large deformation fluid-structure interactions.

Findings

The method accurately captures fluid and structural dynamics during large displacements.

The quasi-Newton scheme demonstrates stability and efficiency in complex simulations.

The approach is applicable to a wide range of membrane and shell problems.

Abstract

This paper presents a general and robust method for the fluid-structure interaction of membranes and shells undergoing large displacement and large added-mass effects by coupling an immersed-boundary method with a shell finite-element model. The immersed boundary method can accurately simulate the fluid velocity and pressure induced by dynamic bodies undergoing large displacements using a computationally efficient pressure projection finite volume solver. The structural solver can be applied to bending and membrane-related problems, making our partitioned solver very general. We use a strongly-coupled algorithm that avoids the expensive computation of the inverse Jacobian within the root-finding iterations by constructing it from input-output pairs of the coupling variables from the previous time steps. Using two examples with large deformations and added mass contributions, we demonstrate that the resulting quasi-Newton scheme is stable, accurate, and computationally efficient.