由於海水碎波模擬往往需花費相當久的時間，且應用上常具有很大限制，針對這個問題，本論文提出一個基於slice的方法來呈現海水碎波自然模擬。首先透過Navier-Stokes方程，精確計算出海水的變化情形，再結合VOF(Volume of fluid) 和一重構自由液面的方法，以快速建構出2D的海水模擬結果。最後對此ㄧ集合之2D模擬結果，採用線性內插和噪音函數(noise function)，來大幅降低模擬時間且達到較佳之模擬效能，並使其可應用在更多的用途上。

The simulation of breaking wave has a computationally intensive application. In order to reduce the computation, this thesis presents a slice-based water simulation method for ocean breaking waves on natural simulation by generating the 2D simulations and then integrating these 2D simulation results into a 3D shape. We first simulate a 2D wave by a 2D Navier-Stokes solver to obtain the varying of ocean. Then, we combine VOF (Volume of fluid) with a new reconstruct free surface method that is a fast 2D simulation. We use linear interpolation with noise function to construct a complete 3D ocean simulation from these 2D simulations. By doing these, one can reduce the computation time and achieve better efficiency.

Chapter 1 Introduction ................................................................................................... 1
Chapter 2 Related work ................................................................................................. 3
2.1 Fluid framework......................................................................................... 3
2.2 Free surface ................................................................................................ 3
2.3 Height field ................................................................................................ 6
2.4 Breaking wave ........................................................................................... 6
Chapter 3 The proposed method .................................................................................. 10
3.1 Grid generation ........................................................................................ 11
3.2 Wave simulation ....................................................................................... 12
3.2.1 Fluid equations ............................................................................. 13
3.2.2 Free surface .................................................................................. 16
3.2.3 Expansion to 3D ........................................................................... 21
3.2.4 Isosurface reconstruction ............................................................. 23
3.2.5 Smoothing the surface.................................................................. 23
3.3 Particle simulation ................................................................................... 24
3.4 Render ...................................................................................................... 26
Chapter 4 Implementation ........................................................................................... 28
4.1 2D simulations ......................................................................................... 28
4.1.1 Initialization ................................................................................. 29
4.1.2 Discretization ............................................................................... 30
4.1.3 Boundary conditions and surface grid ......................................... 32
4.2 GPU implementation ............................................................................... 34
4.3 Results ...................................................................................................... 37
Chapter 5 Conclusions ................................................................................................. 44
References .................................................................................................................... 45

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