摘要
在计算机图形学中，模拟水流动画是一个有意义并且具有挑战性的课题。要得到逼真的水流动画，其中一个关键性的方面在于要模拟出水流的运动形态。本论文用干扰模型来控制水波的产生和模拟各种类型的波，从而能够逼真地制出水流动画。
在我们的水流模型中，水表面看作一个高度场。水流整体可以按微元的观点看成由一系列竖直水柱拼接而成。水流的运动规律由一个浅水波方程，即一个二维的Navier-Stokes方程来描述。
通过浅水波的物理模型，我们可以自动地模拟水波的运动。实验结果表明，水波的运动是逼真的。我们成功地模拟了水波的反射、叠加和绕射现象。
我们借用计算流体动力学中的数值分析工具，对浅水波方程进行数值求解。采用有限体积法求解方程，解稳定并且效率高。而且还可以方便地处理各种复杂的初始条件与边界条件。因此在我们的模型下，水域不再限制成矩形类的区域，而可以是任意单连通的区域。
本论文的前两章介绍水流模拟课题方面的挑战及人们所采用的方法。第三章以后具体地介绍如何利用有限体积法求解浅水波方程得到水波的运动形态，以及如何利用干扰模型扰动方程的数值解来产生各种形状的水波。
The making of water animation is a very interesting and challenging problem in computer graphics. And the modeling behavior of water flow is one of the key aspects in water animation. A disturbance model is offered to simulate the generation of water waves with different kinds of shapes, and to enhance the realistic sense.
In our approach, the water surface is regarded as a height field and the main body of water can be regarded as vertical columns. The motion of water flow can be described by the dynamics fluid equation, such as 2D Navier-Stokes equation.
The motion of water waves can be simulated automatically by the using of physical model bf shallow water. And our demo nicely shows the motion of water waves: reflecting, intervening, circumambulating.
To solve the Navier-Stokes equation, we discrete the water domain into triangular meshes and use a powerful numerical tool named Finite Volume Method. This solver is stable and fast. And it can deal with complicated boundary conditions. The water domain can be any single-continuous field, no matter whether it has holes or not.
In the first part of this thesis, we discuss the challenges of the water simulation scenes and give a detailed survey of this subject. Then in the second part, we describe our work on water animation in details, namely the physical model of shallow-water, the numerical solution of the 2D Navier-Stokes equations using the Finite Volume Method, and the disturbance model which are used to control the behaviors of water waves.
引文
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