A Time-Dependent Wave-Thermoelastic Solid Interaction

TL;DR

This paper develops a combined integral equation method for solving the complex time-dependent interaction between thermoelastic solids and surrounding fluids, providing theoretical analysis, discretization techniques, and numerical validation.

Contribution

It introduces a generalized coupling approach for thermoelastic-fluid interaction problems, including analysis, discretization, and numerical experiments, advancing the computational methods in this field.

Findings

Proved existence and uniqueness of solutions.

Derived error estimates for semi-discretization.

Demonstrated accuracy and efficiency through numerical experiments.

Abstract

This paper presents a combined field and boundary integral equation method for solving the time-dependent scattering problem of a thermoelastic body immersed in a compressible, inviscid and homogeneous fluid. The approach here is a generalization of the coupling procedure employed by the authors for the treatment of the time-dependent fluid-structure interaction problem. Using an integral representation of the solution in the infinite exterior domain occupied by the fluid, the problem is reduced to one defined only over the finite region occupied by the solid, with nonlocal boundary conditions. The nonlocal boundary problem is analyzed with Lubich's approach for time-dependent boundary integral equations. Existence and uniqueness results are established in terms of time-domain data with the aid of Laplace-domain techniques. Galerkin semi-discretization approximations are derived and error estimates are obtained. A full discretization based on the Convolution Quadrature method is also outlined. Some numerical experiments in 2D are also included in order to demonstrate the accuracy and efficiency of the procedure.