UNSTRUCTURED MESH SIZE CONTROL METHOD BASED ON ARTIFICIAL NEURAL NETWORK
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摘要: 网格自动化生成和自适应是制约计算流体力学发展的瓶颈问题之一, 网格生成质量、效率、灵活性、自动化程度和鲁棒性是非结构网格生成的关键问题. 在非结构网格生成中, 网格空间尺度分布控制至关重要, 直接影响网格生成质量、效率和求解精度. 采用传统的背景网格法进行空间尺度分布控制需要在背景网格上求解微分方程得到背景网格上的尺度分布, 再将网格尺度从背景网格插值到真实空间点, 过程十分繁琐且耗时. 本文从效率和自动化角度提出两种网格尺度控制方法, 首先发展了基于径向基函数(RBF)插值的网格尺度控制方法, 通过贪婪算法实现边界参考点序列的精简, 提高了RBF插值的效率. 同时, 还采用人工神经网络进行网格尺度控制, 初步引入相对壁面距离和相对网格尺度作为神经网络输入输出参数, 建立人工神经网络训练模型, 采用商业软件生成二维圆柱和二维翼型非结构三角形网格作为训练样本, 通过训练和学习建立起相对壁面距离和相对网格尺度的神经网络关系. 进一步实现了二维圆柱、不同的二维翼型的尺度预测, RBF方法和神经网络方法的效率与传统背景网格法相比提高了5~10倍, 有助于提高网格生成的效率. 最后, 将方法推广应用于各向异性混合网格尺度预测, 得到的网格质量满足要求.Abstract: Automatic mesh generation and adaptation are bottleneck problems restricting computational fluid dynamics (CFD). Grid quality, efficiency, flexibility, automation level, and robustness are several key issues in grid generation. Mesh size control is significant in unstructured mesh generation which directly impacts the mesh quality, efficiency, and solution accuracy. Controlling mesh size by the background grid method requires mesh size defined on a background mesh by solving differential equations and interpolating from background mesh to specific location, which is very tedious and time-consuming in traditional unstructured grid generation. In this paper, two novel mesh size control methods are proposed in terms of efficiency and automation level. Firstly, radial basis function (RBF) interpolation was developed to control mesh size. In order to improve the efficiency of RBF interpolation, the greedy algorithm was applied to reduce the list of reference nodes. Meanwhile, an artificial neural network (ANN) is used to control the mesh size, relative wall distance, and relative mesh size are introduced as input and output parameters for the ANN. Training models are established and samples (2D cylinder and airfoil grids) are generated by commercial software. The relationship is established between wall distance and mesh size by machine learning. Several meshes are generated with the aforementioned three methods, the results demonstrate that the RBF method and the ANN method are 5-10 times more efficient than the background mesh method, which contributes to efficiency improvement of the grid generation process. Finally, the ANN method is extended to mesh size control of anisotropic hybrid grids, which also obtained meshes of good quality.
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图 1 圆柱算例点源设置及网格生成情况
Figure 1. Nodal source settings and corresponding triangular mesh over a 2D cylinder
图 2 NACA0012算例点源设置及网格生成情况
Figure 2. Nodal source settings and corresponding triangular mesh over NACA0012 airfoil
图 3 30P30N算例点源设置及网格生成情况
Figure 3. Nodal source settings and corresponding triangular mesh over 30P30N airfoil
图 5 圆柱算例精简后的参考点及网格生成情况
Figure 5. Reference nodes corresponding triangular mesh over a 2D cylinder
图 6 NACA0012算例精简后的参考点及网格生成情况
Figure 6. Reference nodes and corresponding triangular mesh over NACA0012 airfoil
图 7 30P30N算例精简后的参考点及网格生成情况
Figure 7. Reference nodes and corresponding triangular mesh over 30P30N airfoil
图 8 网格分布控制与几何特征和流场特征的关系
Figure 8. Relationship between mesh size control, geometry, and flow features
图 10 基于Matlab的人工神经网络训练工具
Figure 10. Artificial neural network training tool based on Matlab
13 ANN模型各向同性网格预测结果
13. Mesh size controlled by ANN model for isotropic triangular grids
图 13 ANN模型各向同性网格预测结果(续)
Figure 13. Mesh size controlled by ANN model for isotropic triangular grids (continued)
图 14 ANN模型各向异性混合网格预测结果
Figure 14. Mesh size controlled by ANN model for anisotropic hybrid grids
表 1 RBF方法参考点的数目及插值耗时
Table 1. Number of reference nodes and time consumption on interpolation
Case No. of Ref. nodes Time consumption/s original selected original selected cylinder 145 12 1.07 0.16 NACA0012 306 142 2.17 1.44 30P30N 340 162 2.39 1.81 
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表 2 ANN输入输出模型
Table 2. Parameter model for artificial neural network
Model input ${\left( {\dfrac{{wdist}}{{{L_{{\rm{r\_d}}}}}}} \right)^{1/6}}$ output $\left\{ {\begin{array}{*{20}{c} } { { {\left[ {\dfrac{ {S{ {p} } } }{ { { {\left( { {L_{ {\rm{r\_w} } } } } \right)}^{1/6} } } } + \dfrac{ {S{ {p} } } }{ { {L_{ {\rm{r\_f} } } } } } } \right]}^{1/6} }, \; wdist \leqslant 0.25{L_{ {\rm{r\_d} } } } } \\ { { {\left[{\dfrac{ {S{ {p} } } }{ { {L_{ {\rm{r\_f} } } } } } } \right]}^{1/6} }\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\rm{ } }, \; wdist > 0.25{L_{ {\rm{r\_d} } } } } \end{array} } \right.$
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表 3 3种方法控制网格尺度耗时对比
Table 3. Efficiency comparison of the three methods
Case Background mesh method (s/cell) RBF method (s/cell) ANN method (s/cell) cylinder 0.60/2889 0.16/2427 0.44/2875 NACA0012 5.31/4680 1.44/4840 0.82/4390 30P30N 14.77/6121 1.81/6050 1.03/4752
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