A fictitious domain finite element method for simulations of fluid-structure interactions: The Navier-Stokes equations coupled with a moving solid

TL;DR

This paper develops a stabilized fictitious domain finite element method for simulating fluid-structure interactions involving Navier-Stokes equations and moving solids, accurately capturing interface stresses and dynamics.

Contribution

It extends a stabilized fictitious domain method to Navier-Stokes coupled with moving solids, providing optimal interface stress approximation and a new algorithm for evolving geometry.

Findings

Accurate prediction of normal stress tensor at the fluid-structure interface.

Effective handling of moving solid dynamics within the fluid flow.

Numerical results on a benchmark problem of a falling disk in a channel.

Abstract

The paper extends a stabilized fictitious domain finite element method initially developed for the Stokes problem to the incompressible Navier-Stokes equations coupled with a moving solid. This method presents the advantage to predict an optimal approximation of the normal stress tensor at the interface. The dynamics of the solid is governed by the Newton's laws and the interface between the fluid and the structure is materialized by a level-set which cuts the elements of the mesh. An algorithm is proposed in order to treat the time evolution of the geometry and numerical results are presented on a classical benchmark of the motion of a disk falling in a channel.