On the interaction problem between a compressible viscous fluid and a nonlinear thermoelastic plate

TL;DR

This paper investigates the complex interaction between a nonlinear thermoelastic plate and a compressible viscous fluid, establishing the existence of weak solutions through a novel operator splitting scheme that decouples the fluid and structure dynamics.

Contribution

It introduces a new operator splitting method for coupled fluid-structure interaction with thermoelastic effects, enabling analysis on a fixed reference domain.

Findings

Existence of weak solutions for the coupled problem.

Development of a time-continuous operator splitting scheme.

Analysis performed on a fixed reference domain for the fluid.

Abstract

In this paper we study the interaction problem between a nonlinear thermoelastic plate and a compressible viscous fluid with the adiabatic constant $\gamma>12/7$. The existence of a weak solution for this problem is obtained by constructing a time-continuous operator splitting scheme that decouples the fluid and the structure. The fluid sub-problem is given on a fixed reference domain in the arbitrary Lagrangian-Eulerian (ALE) formulation, and the continuity equation is damped on this domain as well. This allows the majority of the analysis to be performed on the fixed reference domain, while the convergence of the approximate pressure is obtained on the physical domain.