无网格方法数值结果的可视化方法与实现

科学计算可视化是科学计算中不可缺少的一个组成部分,其主要任务是将数值模拟产生的大量复杂的数据信息通过计算机技术转换成图形、图像信息。无网格方法是一种基于点的数值计算方法,各离散点之间没有联结信息,其数值结果的可视化后处理是一件很困难的事情,尤其当离散点随机分布时,更是如此。Delaunay 三角化是十分理想的散乱数据的可视化工具,它可以根据一组随机分布的离散点数据生成唯一的近似等边三角形。首先介绍了 Voronoi 图与 Delaunay 三角化的基本原理,然后介绍了实现 Delaunay 三角剖分的算法及无网格方法数值结果可视化的实现方法,最后给出了无网格方法可视化的若干应用实例。

VISUALIZATION OF NUMERICAL RESULTS OF MESHLESS METHOD AND ITS REALIZATION

Visualization is an indispensable part in scientific computation. The main task of visualization is to convert large amount of complex data produced by numerical simulation into graphics and/or images by means of computer technology. Meshless method is a numerical simulation method based on discrete points. Since there is no connecting information between each point, it is difficult to realize visualization in the post process of its numerical results, especially in the case of random distribution of discrete points. Delaunay triangulation is a useful tool for the visualization for random distributed points. Unique approximate-equilateral triangles can be obtained from a set of random distributed points by Delaunay triangulation. The basic principles of Voronoi cells and Delaunay triangulation are introduced in this paper. An algorithm of Delaunay triangulation and a way to realize the visualization of numerical results for meshless methods are developed. Several application examples of visualization for meshless method are presented.