Research On Simulation Method For The Elastic Wave And Acoustic Wave Field In Time Domain

The finite-difference time-domain method (FDTD) is one of the most powerful numerical methods for the forward modeling of the electromagnetic wave, elastic wave and acoustic wave propagation and scattering. Through transforming the partial-differential equations to the finite-difference equations, the wave field weight is obtained in the whole space. The FDTD method is a full wave technique that has been widely used to model wave propagation process,and interaction with certain or random object in electromagnetics, acoustics, and elastodynamics. Ultrasonic exploration is an efficacious medical diagnosis technique. The ultrasonic propagation rule in the biology tissue is the physics foundation of the ultrasonic diagnosis. Based on the difference of acoustics characteristics in different biology tissues, it distinguishes the dissimilar tissues, especially the natural tissue from the pathological tissue. The investigation of the ultrasonic propagation rule is important for the medical treatment. First, the method is to develop a complex model of the biology tissue, then to establish the wave equations of this model, and to seek to the acoustic propagation rule in the model base on the known source. Finally the approximate acoustic propagation rule in the biology tissue is found. The FDTD method is an effective technique for the research about ultrasonic propagation rule, because the FDTD is especially appropriate for complex models. The purpose of research on FDTD is to obtain the dynamic computer model of the medical ultrasonic exploration. The various modeling request of the biology tissue come down to the elastic wave and acoustic wave questions. In this thesis, the FDTD theory of the elastic and acoustic wave is mainly discussed, including two dimensional (2D) and three dimensional (3D) FDTD simulations. Then the stability condition of the FDTD method and numerical dispersive are analyzed,and the form and the sort of the power source, and the setting of the source are discussed and adopted. Absorbing boundary condition is an important problem of the FDTD method. Because FDTD simulates the wave field in the finite area, we must mount an especial boundary to absorb the outward travelling wave in the truncation boundary. A perfectly matched layer (PML) absorbing boundary condition is used to absorb the outward travelling wave, which is improved and applied in the elastic and acoustic wave simulation. In the end, the thesis verifies the stability of the elastic and acoustic wave's FDTD method and the absorbing effect of the PML absorbing boundary condition. The result proves that the FDTD programs by the writer run stably and the PML boundary can absorb the outward travelling wave well. Moreover, we simulate the interaction of the elastic wave, acoustic wave and the object through 2D/3D FDTD programs, as well as the propagation of the elastic wave in the heterogeneous layered media.