A parallel solver for fluid structure interaction problems with Lagrange multiplier

TL;DR

This paper introduces a parallel solver for fluid-structure interaction problems using a distributed Lagrange multiplier, finite element discretization, and parallel GMRES, tested on Linux clusters.

Contribution

It presents a novel parallel solver for FSI problems employing a Lagrange multiplier approach with finite element discretization and parallel computing techniques.

Findings

Solver effectively handles FSI problems on Linux clusters.

Finite element discretization ensures accuracy in fluid and structure subproblems.

Parallel GMRES solver accelerates computations significantly.

Abstract

The aim of this work is to present a parallel solver for a formulation of fluid-structure interaction (FSI) problems which makes use of a distributed Lagrange multiplier in the spirit of the fictitious domain method. The fluid subproblem, consisting of the non-stationary Stokes equations, is discretized in space by $\mathcal{Q}_2$-$\mathcal{P}_1$ finite elements, whereas the structure subproblem, consisting of the linear or finite incompressible elasticity equations, is discretized in space by $\mathcal{Q}_1$ finite elements. A first order semi-implicit finite difference scheme is employed for time discretization. The resulting linear system at each time step is solved by a parallel GMRES solver, accelerated by block diagonal or triangular preconditioners. The parallel implementation is based on the PETSc library. Several numerical tests have been performed on Linux clusters to investigate the effectiveness of the proposed FSI solver.