Stable marker-particle method for the Voronoi diagram in a flow field
Stable marker-particle method for the Voronoi diagram in a flow field
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DOI：
10.1016/j.cam.2006.01.035
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发表时间：
2007-05
影响因子：
2.4
通讯作者：
T. Nishida;K. Sugihara;M. Kimura
中科院分区：
文献类型：
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作者：
T. Nishida;K. Sugihara;M. Kimura
流场中的Voronoi图是根据“船帆距离”意义上的最近岛屿将水面细分成区域的网格，其是船逆着水流从一点移动到另一点的最短时间的数学模型。由于等距曲线具有奇异性，所以计算起来比较困难。为了克服这一困难，本文导出了一个新的方程组，它描述了粒子从岛屿边界上的一个给定点开始沿沿着最短路径的运动，从而给出了标记粒子法的一个新的变形。该方法可以独立地跟踪每个粒子，因此即使等距曲线存在奇点，也可以稳定地进行计算。
The Voronoi diagram in a flow field is a tessellation of water surface into regions according to the nearest island in the sense of a “boat-sail distance”, which is a mathematical model of the shortest time for a boat to move from one point to another against the flow of water. The computation of the diagram is not easy, because the equi-distance curves have singularities. To overcome the difficulty, this paper derives a new system of equations that describes the motion of a particle along the shortest path starting at a given point on the boundary of an island, and thus gives a new variant of the marker-particle method. In the proposed method, each particle can be traced independently, and hence the computation can be done stably even though the equi-distance curves have singular points.