Fluid-rigid body interaction in a compressible electrically conducting fluid

TL;DR

This paper proves the existence of weak solutions for a complex system involving multiple rigid bodies interacting with a compressible, electrically conducting fluid and electromagnetic fields, combining mechanical and electromagnetic analysis.

Contribution

It introduces a novel hybrid discrete-continuous approximation method to handle the electromagnetic and fluid interactions in a compressible, conducting fluid with rigid bodies.

Findings

Existence of weak solutions established

Hybrid approximation method developed for electromagnetic interactions

Energy inequality preservation in the approximate system

Abstract

We consider a system of multiple insulating rigid bodies moving inside of an electrically conducting compressible fluid. In this system we take into account the interaction of the fluid with the bodies as well as with the electromagnetic fields trespassing both the fluid and the solids. The main result of this article yields the existence of weak solutions to the system. While the mechanical part of the problem can be dealt with via a classical penalization method, the electromagnetic part requires an approximation by means of a hybrid discrete-continuous in time system: The discrete part of the approximation enables us to handle the solution-dependent test functions in our variational formulation of the induction equation, whereas the continuous part makes sure that the non-negativity of the density and subsequently a meaningful energy inequality is preserved in the approximate system.