On the vanishing rigid body problem in a viscous compressible fluid

In this paper we study the interaction of a small rigid body in a viscous compressible fluid. The system occupies a bounded three dimensional domain. The object it allowed to freely move and its dynamics follows the Newton's laws. We show that as the size of the object converges to zero the system fluid plus rigid body converges to the compressible Navier-Stokes system under some mild lower bound on the mass and the inertia momentum. It is a first result of homogenization in the case of fluid-structure interaction in the compressible situation. As a corollary we slightly improved the result on the influence of a vanishing obstacle in a compressible fluid for gamma >= 6.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

This study investigates the interaction between a small solid body and a viscous compressible fluid. The research focuses on a bounded three-dimensional domain, where the solid body is allowed to move freely according to Newton's laws. The paper presents a result of homogenization in the case of fluid-structure interaction under compressible conditions, showing that the fluid plus rigid body system converges to the compressible Navier-Stokes system as the size of the body approaches zero, subject to certain lower bound conditions on mass and inertia momentum. The study also provides a slight improvement on the understanding of the influence of a vanishing obstacle in a compressible fluid for gamma >= 6.