| The real world is filled with different types of fluid. Such as river, fire and so on all gives us impressive visual effect. So how to simulate these fluids in computer becomes a very popular topic. With the increasement of people's demand for visual result, the traditional key frame technic can't represent complicate fluid. Only physically based fluid simulation can meet people's demand.While physically based fluid simulation needs the solving of Navier-Stokes equation, which is a very complicate difference equation. The classical solution has very low time efficiency, so how to improve the performance of the solution is always a very popular research direction.The main purpose of our paper is to give new solution based on wavelet analysis.Our paper begins with the basic form of Navier-Stokes equation and gives a detail explanation on the variable of the equation. Then we talk about the decomposition of the equation and give the classical solution for the sub equations. After this we introduce our wavelet analysis to improve the solution. For one hand, we make an automatic detail detect method with wavelet analysis, which is the base of multi layer method. And we implement a framework of two layer grid to validate our detail detect method. For another, we transform the velocity into frequency domain by wavelet transform and solve the pressure based on Helmholtz decomposition, which can improve the performance of simulation greatly.Compared with the previous work, our main innovation is that first we make an automatic detail detect method, while the former method is established by people. We detect the details of the fluid by wavelet analysis and make a framework of the multi layer gird method.Secondly, we implement the Helmholtz decomposition with divergence-free wavelet and improve the simulation method greatly. Compared with PCG method, divergence-free wavelet is linear increased when we twice the size of grid. So our wavelet method can be used for large scene easily. |
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