基于光顺的网格优化算法及其关键因素分析
|
摘要
为了探讨单元数、迭代次数以及需求精度等关键因素对于网格优化效果的影响,选用1种较优的四面体单元质量衡量准则建立了网格优化算法的目标函数,在此基础上提出了1种四面体网格质量提高算法,并通过某离心泵蜗壳数值算例对比分析了这些关键因素在网格质量提高和优化耗时方面的异同.结果表明:优化后网格质量在0～0.1区间内的劣质单元数明显减少,同时基于光顺的网格优化算法能够较好地提高网格整体质量,此外,随着单元数的增加,优化后的网格平均质量和优化时间会有所增加,但优化后的最差单元质量出现了波动,存在着1个极值;迭代次数的变化对于优化后的网格质量和优化时间影响较小;需求精度的提高会使得网格质量和优化时间同时增加.
To investigate the influences of element number,iteration number and required accuracy on optimization,a tetrahedron quality metric was chosen to establish objective function to propose a tetrahedral mesh optimization algorithm.Based on volute calculating example of a centrifugal pump,the influences of the key factors on the optimized mesh quality and time consuming were compared.The results show that the poor-quality elements in the range from 0 to 0.1 are significantly reduced.The whole mesh quality can be improved obviously by the mesh optimization-based smoothing algorithm.The average mesh quality and the time cost are increased with the increase of element number,but the worst-quality element is fluctuant with one extremum.Iteration number has slight effect on the mesh quality and time cost.The mesh quality is improved with increased time cost by the increasing of required accuracy.
To investigate the influences of element number,iteration number and required accuracy on optimization,a tetrahedron quality metric was chosen to establish objective function to propose a tetrahedral mesh optimization algorithm.Based on volute calculating example of a centrifugal pump,the influences of the key factors on the optimized mesh quality and time consuming were compared.The results show that the poor-quality elements in the range from 0 to 0.1 are significantly reduced.The whole mesh quality can be improved obviously by the mesh optimization-based smoothing algorithm.The average mesh quality and the time cost are increased with the increase of element number,but the worst-quality element is fluctuant with one extremum.Iteration number has slight effect on the mesh quality and time cost.The mesh quality is improved with increased time cost by the increasing of required accuracy.
引文
[1]Montenegro R,Cascón J M,Escobar J M,et al.An au-tomatic strategy for adaptive tetrahedral mesh generation[J].Applied Numerical Mathematics,2009,59(9):2203-2217.
[2]黄晓东,杜群贵.二维有限元网格的局部加密方法[J].华南理工大学学报:自然科学版,2004,32(12):56-60.Huang Xiaodong,Du Qungui.Local refinement of 2D fi-nite element meshes[J].Journal of South China Univer-sity of Technology:Natural Science Edition,2004,32(12):56-60.(in Chinese)
[3]刘厚林,路明臻,巫进,等.离心泵内部四面体网格的优化算法[J].排灌机械工程学报,2010,28(6):465-469.Liu Houlin,Lu Mingzhen,Wu Jin,et al.Optimizationalgorithm of tetrahedral mesh for centrifugal pumps[J].Journal of Drainage and Irrigation Machinery Enginee-ring,2010,28(6):465-469.(in Chinese)
[4]Ahn H T,Branets L,Carey G F.Moving boundary si-mulations with dynamic mesh smoothing[J].Interna-tional Journal for Numerical Methods in Fluids,2010,64(8):887-907.
[5]Mahmood R,Jimack P K.Locally optimal unstructuredfinite element meshes in 3 dimensions[J].Computersand Structures,2004,82:2105-2116.
[6]Blacker T D,Stephenson M B.Paving:a new approachto automated quadrilateral mesh generation[J].Interna-tional Journal for Numerical Methods in Engineering,1991,32(4):811-847.
[7]Vartziotis D,Wipper J,Schwald B.The geometric ele-ment transformation method for tetrahedral mesh smoo-thing[J].Computer Methods in Applied Mechanics andEngineering,2009,199:169-182.
[8]刘厚林,路明臻,董亮,等.基于错误函数的四面体网格优化算法[J].江苏大学学报:自然科学版,2011,32(1):60-64.Liu Houlin,Lu Mingzhen,Dong Liang,et al.Optimi-zation of tetrahedral mesh based on error function[J].Journal of Jiangsu University:Natural Science Edition,2011,32(1):60-64.(in Chinese)
[9]Escobar J M,Montenegro R,Montero G,et al.Smoo-thing and local refinement techniques for improving tetra-hedral mesh quality[J].Computers and Structures,2005,83:2423-2430.
[10]Parthasarathy V,Kodiyalam S.A constrained optimiza-tion approach to finite element mesh smoothing[J].Fi-nite Elements in Analysis and Design,1991,9(4):309-320.
[11]Freitag L A,Ollivier-Gooch C.Tetrahedral mesh im-provement using swapping and smoothing[J].Interna-tional Journal for Numerical Methods in Engineering,1997,40(21):3979-4002.
[12]Shankap P S,Suzanne M S.A comparison of gradient-and hessian-based optimization methods for tetrahedralmesh quality improvement[C]∥Proceedings of the 18thInternational Meshing Roundtable.USA:Sandia NationalLaboratories,2009:631-648.
[13]董亮,刘厚林,谈明高,等.离心泵四面体网格质量衡量准则及优化算法[J].西安交通大学学报,2011,45(11):31-36.Dong Liang,Liu Houlin,Tan Minggao,et al.Qualitymeasurement criteria and optimization algorithm of tetra-hedral mesh for centrifugal pumps[J].Journal of Xi'anJiao Tong University,2011,45(11):31-36.(in Chi-nese)
[14]Shewchuk J R.What is a good linear element?interpo-lation,conditioning,and quality measures[C]∥Pro-ceedings of the 11th International Meshing Roundtable.USA:Sandia National Laboratories,2002:115-126.
[2]黄晓东,杜群贵.二维有限元网格的局部加密方法[J].华南理工大学学报:自然科学版,2004,32(12):56-60.Huang Xiaodong,Du Qungui.Local refinement of 2D fi-nite element meshes[J].Journal of South China Univer-sity of Technology:Natural Science Edition,2004,32(12):56-60.(in Chinese)
[3]刘厚林,路明臻,巫进,等.离心泵内部四面体网格的优化算法[J].排灌机械工程学报,2010,28(6):465-469.Liu Houlin,Lu Mingzhen,Wu Jin,et al.Optimizationalgorithm of tetrahedral mesh for centrifugal pumps[J].Journal of Drainage and Irrigation Machinery Enginee-ring,2010,28(6):465-469.(in Chinese)
[4]Ahn H T,Branets L,Carey G F.Moving boundary si-mulations with dynamic mesh smoothing[J].Interna-tional Journal for Numerical Methods in Fluids,2010,64(8):887-907.
[5]Mahmood R,Jimack P K.Locally optimal unstructuredfinite element meshes in 3 dimensions[J].Computersand Structures,2004,82:2105-2116.
[6]Blacker T D,Stephenson M B.Paving:a new approachto automated quadrilateral mesh generation[J].Interna-tional Journal for Numerical Methods in Engineering,1991,32(4):811-847.
[7]Vartziotis D,Wipper J,Schwald B.The geometric ele-ment transformation method for tetrahedral mesh smoo-thing[J].Computer Methods in Applied Mechanics andEngineering,2009,199:169-182.
[8]刘厚林,路明臻,董亮,等.基于错误函数的四面体网格优化算法[J].江苏大学学报:自然科学版,2011,32(1):60-64.Liu Houlin,Lu Mingzhen,Dong Liang,et al.Optimi-zation of tetrahedral mesh based on error function[J].Journal of Jiangsu University:Natural Science Edition,2011,32(1):60-64.(in Chinese)
[9]Escobar J M,Montenegro R,Montero G,et al.Smoo-thing and local refinement techniques for improving tetra-hedral mesh quality[J].Computers and Structures,2005,83:2423-2430.
[10]Parthasarathy V,Kodiyalam S.A constrained optimiza-tion approach to finite element mesh smoothing[J].Fi-nite Elements in Analysis and Design,1991,9(4):309-320.
[11]Freitag L A,Ollivier-Gooch C.Tetrahedral mesh im-provement using swapping and smoothing[J].Interna-tional Journal for Numerical Methods in Engineering,1997,40(21):3979-4002.
[12]Shankap P S,Suzanne M S.A comparison of gradient-and hessian-based optimization methods for tetrahedralmesh quality improvement[C]∥Proceedings of the 18thInternational Meshing Roundtable.USA:Sandia NationalLaboratories,2009:631-648.
[13]董亮,刘厚林,谈明高,等.离心泵四面体网格质量衡量准则及优化算法[J].西安交通大学学报,2011,45(11):31-36.Dong Liang,Liu Houlin,Tan Minggao,et al.Qualitymeasurement criteria and optimization algorithm of tetra-hedral mesh for centrifugal pumps[J].Journal of Xi'anJiao Tong University,2011,45(11):31-36.(in Chi-nese)
[14]Shewchuk J R.What is a good linear element?interpo-lation,conditioning,and quality measures[C]∥Pro-ceedings of the 11th International Meshing Roundtable.USA:Sandia National Laboratories,2002:115-126.