中文摘要：

为解决光滑质点流体动力学方法数值模拟过程中出现的数值断裂问题，提出一种基于Delaunay三角剖分及其对偶形式最近点意义下的Voronoi图的粒子产生和消除技术，对产生数值断裂的区域重新布点。同时讨论此技术实施过程中伴随的质量、动量和能量守恒问题的解决办法。通过典型数值算例的模拟分析可以看出，粒子产生和消除技术可以有效地解决数值断裂问题。当考察程序的相对运行时间随模型粒子数目的变化时发现，只使用粒子产生技术时，由于粒子数目大量增加使程序运行时间急剧增加。而同时使用粒子产生和消除技术时，由于粒子数目基本不变，使程序运行时间只增加百分之十左右。当考察在整个程序的运行过程中模型总能量的变化时发现，使用文中提出的守恒问题解决办法，可以基本保证能量始终守恒。

英文摘要：

To solve the problem of numerical fracture in the process of numerical simulation of smoothed particle hydrodynamics method, based on Delaunay triangulation and Voronoi diagram, a new technique of particle generation and particle elimination was presented to redistribute the scattered particles of the numerical fracture region. And meanwhile, the conservation of mass, momentum and energy were discussed. Two typical numerical examples were simulated and the results show that the problem of numerical fracture is solved effectively. When investigate the change of relative rtmtime along with the particle number of the model, if only use particle generation technique, due to the increase of particle number, the runtime go up sharply. But if both of the particle generation and particle elimination techniques are used, because of the invariability of particle number, the nmtime increases by only about 10%. This percentage is acceptable obviously. When investigate the change of total energy all through the process, results show that the total energy is almost the same from beginning to the end of the whole process.