A stable partitioned FSI algorithm for incompressible flow and deforming beams

TL;DR

This paper introduces a second-order accurate, stable added-mass partitioned algorithm for fluid-structure interaction problems coupling incompressible flows with elastic beams, effective even with light structures and strong added-mass effects.

Contribution

The paper presents a novel stable AMP scheme for FSI problems that avoids sub-time-step iterations and handles large deformations with a mixed Eulerian-Lagrangian approach.

Findings

The AMP scheme is unconditionally stable regardless of fluid-to-structure mass ratio.

The scheme achieves second-order accuracy in both space and time.

Benchmark problems confirm the stability and accuracy of the proposed method.

Abstract

An added-mass partitioned (AMP) algorithm is described for solving fluid-structure interaction (FSI) problems coupling incompressible flows with thin elastic structures undergoing finite deformations. The new AMP scheme is fully second-order accurate and stable, without sub-time-step iterations, even for very light structures when added-mass effects are strong. The fluid, governed by the incompressible Navier-Stokes equations, is solved in velocity-pressure form using a fractional-step method; large deformations are treated with a mixed Eulerian-Lagrangian approach on deforming composite grids. The motion of the thin structure is governed by a generalized Euler-Bernoulli beam model, and these equations are solved in a Lagrangian frame using two approaches, one based on finite differences and the other on finite elements. Special treatment of the AMP condition is required to couple the finite-element beam solver with the finite-difference-based fluid solver, and two coupling approaches are described. A normal-mode stability analysis is performed for a linearized model problem involving a beam separating two fluid domains, and it is shown that the AMP scheme is stable independent of the ratio of the mass of the fluid to that of the structure. A traditional partitioned (TP) scheme using a Dirichlet-Neumann coupling for the same model problem is shown to be unconditionally unstable if the added mass of the fluid is too large. A series of benchmark problems of increasing complexity are considered to illustrate the behavior of the AMP algorithm, and to compare the behavior with that of the TP scheme. The results of all these benchmark problems verify the stability and accuracy of the AMP scheme. Results for one benchmark problem modeling blood flow in a deforming artery are also compared with corresponding results available in the literature.