Time-Dependent Fluid-Structure Interaction

TL;DR

This paper develops a mathematical framework for analyzing how acoustic waves scatter off elastic bodies in fluids over time, using a coupling approach and Laplace transform techniques, to support numerical methods like FEM and BEM.

Contribution

It introduces a novel reduction of the time-dependent fluid-structure interaction problem to a nonlocal initial-boundary problem and analyzes it using the Lubich approach in the time domain.

Findings

Provides a mathematical foundation for time-dependent fluid-structure interaction analysis.

Demonstrates the use of Laplace transform and Lubich approach for nonlocal problems.

Supports convolution quadrature coupling of FEM and BEM for numerical solutions.

Abstract

The problem of determining the manner in which an incoming acoustic wave is scattered by an elastic body immersed in a fluid is one of central importance in detecting and identifying submerged objects. The problem is generally referred to as a fluid-structure interaction and is mathematically formulated as a time-dependent transmission problem. In this paper, we consider a typical fluid-structure interaction problem by using a coupling procedure which reduces the problem to a nonlocal initial-boundary problem in the elastic body with a system of integral equations on the interface between the domains occupied by the elastic body and the fluid. We analyze this nonlocal problem by the Lubich approach via the Laplace transform, an essential feature of which is that it works directly on data in the time domain rather than in the transformed domain. Our results may serve as a mathematical foundation for treating time-dependent fluid-structure interaction problems by convolution quadrature coupling of FEM and BEM.