Existence of a weak solution to a nonlinear fluid-structure interaction problem with heat exchange

TL;DR

This paper proves the existence of a weak solution for a complex nonlinear fluid-structure interaction problem involving a thermoelastic shell and a heat-conducting fluid with heat exchange, using innovative approximation techniques.

Contribution

It introduces a novel approach combining decoupling, penalization, and domain extension to analyze a nonlinear moving boundary fluid-structure interaction with heat exchange.

Findings

Existence of a weak solution established.

Simplified analysis through new approximation scheme.

Applicable to complex heat-exchanging fluid-structure systems.

Abstract

In this paper, we study a nonlinear interaction problem between a thermoelastic shell and a heat-conducting fluid. The shell is governed by linear thermoelasticity equations and encompasses a time-dependent domain which is filled with a fluid governed by the full Navier-Stokes-Fourier system. The fluid and the shell are fully coupled, giving rise to a novel nonlinear moving boundary fluid-structure interaction problem involving heat exchange. The existence of a weak solution is obtained by combining three approximation techniques -- decoupling, penalization and domain extension. This approximation scheme allows us to use the methods already developed for fluids on moving domains, thus drastically simplifying the analysis at hand.