A coupled 3D fluid-elastic wave propagation model: mathematical formulation and analysis

Abstract

A three-dimensional mathematical model is developed for handling environmental interactions in the ocean between a fluid medium and an elastic bottom. The model is a combination of three-dimensional wave propagaion models in both the fluid and the elastic media, together with the incorporation of a set of fluid-elastic interface conditons. A complete theory with regard to the mathematical formulation of the fluid and elastic models is discussed, along with an error analyiss, and a description of the derivation of the fluid-elactic interface equations is given. A ordinary differential equation (ODE) method in conjunction with a finite difference marching scheme to obtain the numerical solution of the complete representative system of coupled fluid-elastic wave equations is outlined; moreover, the theory with regard to the stability and consistency of the marching scheme is discussed. The major development of this paper is the combination of the fluid equations, the elastic equations and the set of fluid-elastic interface conditions into a single unified three-dimensional model capable of applications to realistic fluid-elastic interactions in the ocean environment.

Keywords:

• Wave propagation
• fluid mechanics
• elasticity
• parabolic equations