Voronoi图在移动粒子半隐式法中的应用

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关键词：Voronoi图；MPS法；表面粒子判定；粒子迁移；邻近粒子搜索中图分类号：O242；TP301.6文献标志码：ADOI： 10.7652/xjtuxb202605011 文章编号：0253-987X（2026）05-0111-09

Applications of Voronoi Diagram in the Moving Particle Semi-Implicit Method

ZHOU Ziqi，SUN Yijie， SUN Zhongguo，XI Guang （School of Energy and Power Engineering，Xi'an Jiaotong University， Xi'an 7loo49，China）

Abstract：To optimize the algorithms for establishing and analyzing spatial topology in the moving particle semi-implicit （MPS） method，the Voronoi diagram to three key components is applied： neighbor particle search，surface particle detection， and particle shifting. The specific approaches are as follows： a particle Voronoi diagram is constructed to facilitate neighbor particle search by leveraging its inherent topological relationships； a novel method based on Voronoi cell structure is proposed to address the challenge of surface particle detection； and a particle shifting scheme derived from the Voronoi diagram is developed by integrating the Lloyd relaxation algorithm with the Green-Gauss formula. The results demonstrate that： the Voronoi-based particle search achieves an efficiency improvement of over l59 times compared to the traditional all-pair search method；the Voronoi-based surface particle detection is more accurate than the conventional particle number density method and computes 43.3 times faster than the geometric method; furthermore，the Voronoi-based particle shifting effectively reduces system disturbance while preserving the smoothness and non-overlapping characteristics of the free surface，also yielding a computational eficiency advantage exceeding 6 times compared to traditional shifting approaches. In conclusion， the proficient spatial partitioning properties of the Voronoi diagram present promising potential for its application within the MPS framework.

Keywords： Voronoi diagram；MPS method;surface particle detection； particle shifting； neighboringparticles searching

光滑粒子流体动力学（SPH）[1-2]和移动粒子半隐式法（MPS）[3-4]属于拉格朗日无网格粒子方法。（剩余15209字）