A parallel solver for FSI problems with fictitious domain approach

TL;DR

The paper tackles efficient parallel solution of fluid–structure interaction problems modeled with a fictitious-domain approach and distributed Lagrange multipliers, where a time-dependent incompressible Navier–Stokes fluid interacts with an elastic solid. It develops a PETSc-based solver for the resulting saddle-point systems, comparing a block-diagonal and a block-triangular preconditioner on a discretization that uses a $(\mathcal{Q}_2,\mathcal{P}_1)$ fluid pair and a $\mathcal{Q}_1$ solid discretization with a semi-implicit Backward Euler time stepping. The study demonstrates that the block-triangular preconditioner offers robust performance under mesh refinement and exhibits good weak scalability for both linear and nonlinear solids, while the block-diagonal approach can fail to scale. A significant practical finding is that the coupling-matrix assembly remains a bottleneck, motivating future work on more scalable coupling algorithms and extending the framework to 3D and more complex constitutive laws. The results establish the viability of a parallel fictitious-domain FSI solver for large-scale simulations on modern clusters.

Abstract

We present and analyze a parallel solver for the solution of fluid structure interaction problems described by a fictitious domain approach. In particular, the fluid is modeled by the non-stationary incompressible Navier-Stokes equations, while the solid evolution is represented by the elasticity equations. The parallel implementation is based on the PETSc library and the solver has been tested in terms of robustness with respect to mesh refinement and weak scalability by running simulations on a Linux cluster.

Figures (2)

• Figure 1: Four snapshots of the evolution of the structure with linear constitutive law.
• Figure 2: Four snapshots of the evolution of the structure with nonlinear constitutive law.