基于离散模型的二维水波实时动态模拟方法

Realtime dynamic simulation of 2-D water waves based on discrete model

从小振幅二维水波的偏微分运动方程出发,通过建立水面模型的离散点栅格结构,从时间和空间两个方面对连续的水波运动过程进行离散化处理,推导出水波微分方程的差分逼近系统,得出在任意离散时刻的水波曲面上,任一采样点处的垂直偏移与法矢量的迭代计算方法,以及保证离散系统迭代计算具有稳定性的系统参数约束条件。试算结果表明,在计算机图形硬件支持下,离散模型系统可以对点振源和线振源引起的水波进行实时真实感动态绘制。该算法可用于三维水环境模拟、动态水面仿真等领域。

Based on the partial derivative equation for 2-D small amplitude water wave movement a difference approaching system for calculating the derivative equation of water wave by establishing the grid structure of discrete points in water surface model is proposed. The continuous movement process of water wave is discretized both in space and time. The iterated calculation of vertical deflection and normal direction vector on water surface at arbitrary point and arbitrary, moment can be carried out. The constraint condition of parameters in the iteration calculation for ensuring the stability of system is derived. The trial calculation shows that under the support of printing hardware the proposed method can efficiently simulate and derive the real 2-D water wave pictures caused by point or line vibration sources in realtime.