Bubble Model Based Grid Generation and Grid Size Control over Free-Form Surface
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摘要: 为了在自由曲面上生成形状规整、大小可控的三角形网格，提出一种基于气泡运动模型的网格自动生成方法. 将适量的网格点布置在离散化的曲面上，并模拟为弹性气泡. 引入气泡间的相互作用力和曲面对气泡的吸附力，得到各气泡的运动控制方程. 采用数值方法近似求解气泡系统的平衡状态. 将平衡后的气泡中心用曲面Delaunay法连接成曲面上的三角形网格. 在气泡模型中，通过相对半径函数控制各气泡的相对大小，进而实现对网格大小的调控. 通过在相对半径函数中考虑气泡中心到特定点或线的距离、参考线或曲面的曲率等因素的影响，生成网格大小与曲面特征相适应的三角形网格. 6个算例结果表明，该方法生成的网格形状规整、疏密有致，其形状质量指标都高于0.97；该方法为网格结构的设计提供了参考.Abstract: To generate triangular grids with regular shapes and adaptive sizes over free-form surfaces, an automatic grid generation method is presented on the basis of a bubble dynamic model. Grid nodes were first decorated on the discretized surface according to certain rule, and were regarded as elastic bubbles. The inter-bubble forces and the forces from surface adsorption were introduced. The motion control equations of bubbles were established. Then, the equilibrium state of the bubble system was acquired by the numerical simulation algorithm. Finally, the centers of balanced bubbles were connected into a triangular grid by an extended Delaunay method. In the bubble model, the size of a bubble is determined by the relative radius function. And the control of the grid size is realized by adjusting the bubble size. Through the relative radius function factoring in the distance from each bubble center to selected points or curves, the curvature of reference curves or the surface and so on, the method can generate triangular grids with edges adapted to the surface features. Six cases have demonstrated that the grids generated by the proposed method have regular shapes and adaptive sizes, with their shape quality indexes all higher than 0.97. The method provides the convenience for the design of grid structures.
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Key words:
- free-form surface /
- grid structure /
- grid generation /
- bubble-like method /
- grid control
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表 1 网格质量评价
Table 1. Quality evaluation of grids
对象 调控方式 杆长 形状质量指标 平均值/m 离散系数 平均值 方差/× 10−4 M1 均匀 5.11 0.063 0.988 2.92 M2 距离 2.49 0.184 0.978 6.32 M3 距离 3.39 0.149 0.976 7.68 M4 曲率 2.56 0.141 0.977 6.82 M5 综合 3.89 0.151 0.977 6.62 M6 均匀 5.25 0.162 0.935 28.6 
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