Numerical Simulation of Fluid-Structure Interaction Problems with Hyperelastic Models: A Monolithic Approach

TL;DR

This paper presents a monolithic numerical approach for fluid-structure interaction problems involving hyperelastic models, utilizing Newton's method and advanced solvers, and compares it with partitioned methods.

Contribution

It introduces a monolithic solution framework for coupled FSI problems with hyperelastic materials, including solver strategies and comparative analysis.

Findings

Monolithic approach effectively solves FSI problems with hyperelastic models.

Preconditioned Krylov, algebraic multigrid, and multilevel methods improve linear system solutions.

Comparison shows differences between monolithic and partitioned approaches.

Abstract

In this paper, we consider a monolithic approach to handle coupled fluid-structure interaction problems with different hyperelastic models in an all-at-once manner. We apply Newton's method in the outer iteration dealing with nonlinearities of the coupled system. We discuss preconditioned Krylov sub-space, algebraic multigrid and algebraic multilevel methods for solving the linearized algebraic equations. Finally, we compare the results of the monolithic approach with those of the corresponding partitioned approach that we studied in our previous work.