Progress on analytical models for refraction and diffraction of water waves 折射和衍射現象的解析模型的研究進展
Finite difference method can deal with regular boundary conditions . in this paper , we discrete the water domain into rectangular meshes , and simulate the propagation , reflection and diffraction of water waves . we just specify waves source , the movement of water waves can be simulated automatically 有限差分方法能夠處理具有規則邊界水域的水流現象,在本文中,我們把求解的水域離散成結構矩形網格,對水流的折射、反射、繞射等水流現象進行了動畫模擬,我們僅僅指定產生水流動畫的波源,水流動畫的細節均由數值方法產生,不需要人工的干預。
According to different water phenomena , we use two different method to produce waves source : the first method is by specifying the boundary conditions and initialization conditions , this method simulate the dam breaking , reflection and diffraction of water waves ; the second method is by specifying disturbance model , this method simulate water droplets , waterfall , waves of ship ; in the first part of this thesis , we discuss the prevalent methods of the simulation of water scenes , in the second part of this thesis , we describe the numerical methods of solving the shallow water equations using the finite difference method and the finite volume method respectively , in the third part of this thesis , we simulate some realistically liquid phenomena such as rain droplets , the waves of ship , dam breaking etc 產生水波首先要有波源,設置不同的波源便可以得到不同的水流情形,我們用兩種方法來產生波源:一種是通過設置邊界條件和初始條件產生,這種方法用于模擬潰壩波的反射、折射等現象;另一種是通過擾動控制產生,這種方法用于模擬雨滴、瀑布、船波等自然現象。本論文的第一部分我們討論了目前水動畫模擬常用的幾種方法;在第二部分討論了我們所使用的兩類數值方法:有限差分方法和有限體積方法;在第三部分我們模擬了雨滴、船波、潰壩波等一些水流現象。