Numerical analysis of a penalization method for the three-dimensional motion of a rigid body in an incompressible viscous fluid

TL;DR

This paper develops and analyzes a penalization method for simulating the three-dimensional motion of a rigid body in an incompressible viscous fluid, using a level set approach to handle the fluid-solid interface.

Contribution

It extends existing penalization techniques to 3D fluid-rigid body interactions with a level set interface, providing convergence analysis and numerical validation.

Findings

Convergence of the proposed method demonstrated through numerical experiments.

The method effectively captures the fluid-solid interface dynamics.

Discussion relates the results to existing existence theorems.

Abstract

We present and analyze a penalization method wich extends the the method of [1] to the case of a rigid body moving freely in an incompressible fluid. The fluid-solid system is viewed as a single variable density flow with an interface captured by a level set method. The solid velocity is computed by averaging at avery time the flow velocity in the solid phase. This velocity is used to penalize the flow velocity at the fluid-solid interface and to move the interface. Numerical illustrations are provided to illustrate our convergence result. A discussion of our result in the light of existing existence results is also given. [1] Ph. Angot, C.-H. Bruneau and P. Fabrie, A penalization method to take into account obstacles in incompressible viscous flows, Numer. Math. 81: 497--520 (1999)