Rigid body in compressible flow with general inflow-outflow boundary data

TL;DR

This paper proves the existence of weak solutions for the motion of a rigid body in a compressible viscous fluid within a bounded domain, under specific boundary conditions, avoiding boundary contact.

Contribution

It establishes the existence of weak solutions for a coupled fluid-structure interaction problem with general inflow-outflow boundary data in compressible Navier-Stokes flow.

Findings

Existence of weak solutions proven for the coupled system.

Solutions exist as long as the rigid body does not contact the boundary.

The boundary conditions include prescribed inflow velocity and density, with no-slip at the interface.

Abstract

We study the motion of a rigid body within a compressible, isentropic, and viscous fluid contained in a fixed bounded domain $\Omega \subset \mathbb{R}^3$. The fluid's behavior is described by the Navier-Stokes equations, while the motion of the rigid body is governed by ordinary differential equations representing the conservation of linear and angular momentum. We prescribe a time-independent fluid velocity along the boundary of $\Omega$ and a time-independent fluid density at the inflow boundary of $\Omega$. Additionally, we assume a no-slip boundary condition at the interface between the fluid and the rigid body. We prove existence of a weak solution to the given problem within a time interval where the rigid body does not touch the boundary $\partial\Omega$.