Exploiting high-contrast Stokes preconditioners to efficiently solve incompressible fluid-structure interaction problems

Abstract

In this work, we develop a new algorithm to solve large-scale incompressible time-dependent fluid--structure interaction (FSI) problems using a matrix-free finite element method in arbitrary Lagrangian--Eulerian (ALE) frame of reference. We derive a semi-implicit time integration scheme which improves the geometry-convective explicit (GCE) scheme for problems involving the interaction between incompressible hyperelastic solids and incompressible fluids. The proposed algorithm relies on the reformulation of the time-discrete problem as a generalized Stokes problem with strongly variable coefficients, for which optimal preconditioners have recently been developed. The resulting algorithm is scalable, optimal, and robust: we test our implementation on model problems that mimic classical Turek benchmarks in two and three dimensions, and investigate timing and scalability results.

arXiv comment24 pages, 9 figures, 9 tables

References in corpus (4)

• The deal.II finite element library: design, features, and insights
• Well-posedness and Robust Preconditioners for the Discretized Fluid-Structure Interaction Systems
• A parallel Newton multigrid framework for monolithic fluid-structure interactions
• Modeling and Simulation for Fluid-Rotating Structure Interaction

Cited by in corpus (1)

• Smoothers with localized residual computations for geometric multigrid methods