近年来在计算机图形学领域中，基于物理的流体动画受到的重视程度越来越高,水墨动画与小尺度流体模拟作为流体动画中的一个研究方向，也得到了很多研究者的重视。基于物理的流体动画模拟首先对需要模拟的场景进行物理建模，然后采用数值方法求解控制方程，最后再使用图形学的方法进行可视化绘制，基于物理的流体模拟使用的控制方程是计算流体力学中广泛使用的纳维斯托克斯方程（NSE）。目前，基于物理的流体动画模拟主要有两个方面的制约，其一是对复杂场景的物理建模，其二是由于纳维斯托克斯方程的复杂性而导致对计算能力的较高要求。本文首先探讨了基于物理的流体动画模拟的一些基本方法，基于物理的方法主要包括基于欧拉的方法以及基于拉格朗日的方法这两类。本文使用基于网格的方法求解NSE方程，进而对中国传统的水墨动画中的水墨之间的相互作用进行模拟，将水墨滴入水中的运动过程分解为墨汁在水中受到外力运动、扩散、平流以及对流运动等一系列的组合。使用了一种基于网格的半拉格朗日法来求解纳维斯托克斯方程，实现了在二维和三维两种不同情形下的水墨动画模拟。其次，本文对基于粒子的光滑粒子流体动力学（SPH）方法进行探讨研究，针对传统的SPH方法求解压力时的不稳定的问题，本文使用预测修正的不可压缩光滑粒子动力学方法（PCISPH）来求解压力；同时，本文对小尺度流体的表面张力的形成进行了研究，实现了一种将颜色场梯度计算与分子间相互作用力模型相结合的表面张力计算方法来计算表面张力。本文首先对二维平面上的小尺度流体进行模拟，验证了本文所使用的计算方法的有效性，再将其扩展到三维情形中，实现了水滴滴入水面的动画模拟；由于粒子数目较大时对计算性能的要求很高，本文使用GPU加速技术对三维动画模拟的计算以及最后的流体的表面重构与绘制进行了加速，使整个模拟过程基本达到实时的效果。

Recently the physical-based fluid simulation gets higher attention in computer animation area. As Chinese Ink simulation and little scale fluid simulation are important parts of fluid simulation, they also get more attention. The physical-based fluid simulation mainly uses the equations called Navier-Stokes Equations to describe the motion of fluid firstly used by the researchers in CFD. When we use physical models to simulate the fluid, firstly, we should build physical models for the scenes should be simulated. Then we use the numerical calculation method to solve the contral equations. The final step is to render the whole scenes. The main difficulties to use physical methods to simulate fluid are: the difficulties in building physical models for complex scenes and the computing resources needed to calculate the control functions.Firstly, we simulate the motion of ink putting in the water which is a common case in the Chinese tradition ink painting. We consider the process of ink as a series of motions like moved by the extern forces, the diffusion and advection. This article uses a half- Lagrange method to calculate the NSE equations, and we realize a 2D and a 3D simulator to simulate the 2D condition ink motion and 3D ink motion. For the secondly, we have a research on the method of SPH(Smoothed Particle Hydrodynamics), which is a Lagrange method, as the tradition SPH method have a disadvantage in compute the pressure, we use a PCISPH（Predictive corrective incompressible SPH）model to reduce the errors. Furthermore, we have a research on the surface tension of the fluid, and implement a method combining the Color Field Method and Interactions with Interaction Forces model to calculate the surface tension in our SPH model. We do some experiment to make sure the effective of our method in 2D condition and finally we realize a 3D animation of a water drop drops in the water surface. For we have implemented a larger scale of particles and use Marching Cubes to help render , we use the GPU to help calculate and render, the whole system can run at a real time.