The Simulation, Based On The Finite Difference Method And Finite Volume Method Flow Animation

The behavior of water flow is one of the interesting aspects of water animation. In this paper, we simulate the realistically liquid phenomena. It is based on the shallow water equations.We use two numerical methods to solve the shallow water equations :one is finite difference method; the other is finite volume method.Finite difference method can deal with regular boundary conditions. In this paper, we discrete the water domain into rectangular meshes, and simulate the propagation, reflection and diffraction of water waves. We just specify waves source, the movement of water waves can be simulated automatically. Our demo nicely shows the motion of waters. All the movement needs no artificial intervention.Finite volume method can deal with irregular boundary conditions. In this paper, we discrete the water domain into triangular meshes, and simulate dam breaking, water droplets. The same as Finite difference method, we just specify waves source, the movement of water waves can be simulated automatically. Our demo nicely shows the motion of waters. All the movement needs also no artificial intervention.According to different water phenomena, we use two different method to produce waves source: the first method is by specifying the boundary conditions and initialization conditions, this method simulate the dam breaking, reflection and diffraction of water waves; the second method is by specifying disturbance model, this method simulate water droplets, waterfall, waves of ship;In the first part of this thesis, we discuss the prevalent methods of the simulation of water scenes, in the second part of this thesis, we describe the numerical methods of solving the shallow water equations using the finite difference method and the Finite Volume Method respectively, in the third part of this thesis, we simulate some realistically liquid phenomena such as rain droplets, the waves of ship, dam breaking etc.