Finite Difference Methods For Time-harmonic Wave Equations In Fluid-solid Interaction Field

Fluid-solid interaction equations are used to describe the scattering of time-harmonic acoustic waves and elastic waves in fluid-solid interaction field; it has important practical value in many scientific and engineering fields. In this thesis, we focus attention on the fluid-solid interaction model that is the scattering of acoustic wave by an elastic body immersed in a fluid. There are different numerical methods been proposed for solving this model, such as finite element methods, boundary element methods and the coupling strategy of finite element method and boundary element method. This thesis discusses to simulate the fluid-solid interaction model by using the finite difference method.This thesis is organized as follows: in the first chapter, we introduce the background and the recent developments of fluid-solid interaction equations and the main work of this thesis: using finite difference methods to deal with fluid-solid interaction equations. In second chapter, we simply state the model that we discuss in this thesis and present different algorithms. Because of the complexity of the fluid-solid interaction model, first we present standard difference scheme, compact difference scheme and new difference scheme of a time-harmonic fluid-solid interaction model in one dimension, and then we deal with the two-dimensional case. Finally, in the third chapter, we present several numerical examples to illustrate the feasibility and efficiency of the proposed schemes.By comparison of the different schemes, we can see that the new difference scheme has a 2n-order of rate of convergence, a simple structure and a better accuracy comparing with the schemes that have the same order in one dimension. Moreover, the new scheme is efficient for the case that the wave numbers are very large, namely, the new scheme eliminates the numerical pollution.