基于SPH方法的滴水涟漪动画模拟  

Simulation of Ripples Based on Smoothed Particle Hydrodynamics Method

作　　者：李玉梅[1] 汪继文[1] 

机构地区：[1]安徽大学计算智能与信号处理教育部重点实验室

出　　处：《计算机技术与发展》2010年第5期56-58,62,共4页Computer Technology and Development

基　　金：安徽省自然科学基金(090412045)

摘　　要：光滑粒子流体动力学(Smoothed Particle Hydrodynamics,SPH)方法是一种新近发展的可用于流体模拟的无网格数值方法。文中基于SPH方法的基本原理,利用SPH方法求解描述水流现象的二维浅水波方程,根据具体模型使用Mon-aghan人工粘性的变形形式,有效地防止了相互靠近粒子的穿透,消除了SPH方法在模拟流体动力学问题时产生的数值振荡。通过使用可变光滑长度,使邻近粒子的数量保持相对稳定,提高了求解的计算效率和精度。同时,对光滑长度进行了修正以获取对称光滑长度,保持了粒子间相互作用对称性。全面考虑了各种定解条件的设置,对水滴的运动进行了模拟,SPH模拟结果与有限差分法、有限体积法结果非常吻合,验证了方法的准确性,为SPH方法的进一步发展和广泛运用奠定了基础。Smoothed particle hydrodynamics（SPH） method is a newly developed meshless numerical method which can be used for the simulation of fluid.In this paper,the SPH method is applied to solve the two-dimensional shallow water equation based on the basic principles of SPH,distortion of Monaghan artificial viscosity is introduced to prevent unphysical penetration for particles approaching each other and remove numerical oscillation in hydrodynamics simulations using SPH.One approach to dynamically evolve the smoothing length is proposed to keep the number of neighboring particles relatively constant and improve the efficiency of the computation and the accuracy of the solution.Meanwhile,in order to preserve the symmetry of particle interaction,some ways to perform the modification are used to produce a symmetric smoothing length.A variety of settings solution conditions will be fully taken into account,the movement of water droplets have been simulated,SPH simulation results is similar with the results obtained by finite difference method and finite volume method.The results verified the accuracy of the method.It laid the foundation for the further development and wider application of SPH method.

关 键 词：光滑粒子流体动力学方法 浅水波方程 光滑核函数 水波动画 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]