Water Animation Based On Composite Numerical Methods

With the development of Computer Graphics people are more and more interested in simulating of natural phenomena ,in which making animation of water flow becomes a popular issue. To produce realistic scene in water animation, the behavior of water flow is one of the most important aspects .In the paper, we describe the behavior of water flow by a fluid dynamics equation such as 2D Navier-Stokes equation. Because of its accordance with the order of nature, we can get good result in invoking waves which have different shapes. In the model, the water surface is taken as a height field and water body is discrected into a set of vertical volumes.To resolve the 2D Navier-Stokes equation, we use two numerical methods which are composite finite difference method and composite finite volume method. They are both formed by global composition of Lax-Wendroff (LW) scheme and Lax-Friedrichs (LF) scheme . The finite difference method is simple and fit for regular domain, and the finite volume method is presented on unstructured triangular meshs , so it can be applied for any compolicated domain. We know LW scheme is a second-order scheme, inclined to produce oscillation around shocks. LF scheme cause no oscillation but it is excessively dissipative. So the composite method will eliminate their respective defects and it is formed by global composition of several Lax-Wendroff type steps followd by a diffusive Lax-Friedrichs type step, which filters out the oscillation around shocks.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 the paper , we simulate some familiar liquid phenomenan such as water droplets,lD dambreak and two typical examples of supercritical channel flows.There are three parts in the paper and their contents are organized as follow. In the first part,we introduce the prevalent methods and tools of simulation of water flow, in the second part we introduce the two numerical methods used inour experiments,in the last part we illustrate the results of the simulation of water flow.