Study Of 3D Visualization Of Water Waves Based On N-S Equation

With the development of Computer Graphics and hardware, people are more and more interested in simulating of natural phenomena, in which making animation of water flow becomes a popular issue. This thesis is a part of Wangkuai-Xidayang reservoir of interbasin water transfer project dynamic simulation, and is the most important part. Based on hydrodynamics N-S equations, established adaptive simulation model. It provide a visualized 3D pratigue platform for decision making and construction during water transfer project. It also provide technology supports for higher level water dispatching system dynamics model.For the simulation of dynamic water flow based on physic model, a popular method is functional construction in mathematic, through that method can get a static water waves picture. In this thesis, start with law of flow movement equation, by Composite Finite Difference Method and Finite Volume Method to solve the equation, finally use OpenGL to Process dynamic visualization. Thus, not only a static water-waves picture is gained, but also water wave animation can be got.To produce realistic scene in water animation, the behavior of water flow is one of the most important aspects. 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. To solve the Navier-Stokes equation, discrete the water domain into triangular meshes and use a powerful numerical tool named Finite Volume Method.Using the tracer tool OpenGL to make the data in each time step visible, we can see the scenes of the behavior of water flow. In our approach, we simulate some familiar liquid phenomena such as water droplets, water surface under falling rain, hydraulic jump, etc.In the first part of this thesis, 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 2D Navier-Stokes equation using the Finite Volume Method and Composite Finite Difference Method, and the disturbance model which are used to control the behaviors of water waves, in the last part we illustrate the results of the simulation of water flow.