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三维稳态对流扩散问题的无网格求解算法研究

张小华 邓霁恒

张小华, 邓霁恒. 三维稳态对流扩散问题的无网格求解算法研究[J]. 应用数学和力学, 2014, 35(11): 1249-1258. doi: 10.3879/j.issn.1000-0887.2014.11.008
引用本文: 张小华, 邓霁恒. 三维稳态对流扩散问题的无网格求解算法研究[J]. 应用数学和力学, 2014, 35(11): 1249-1258. doi: 10.3879/j.issn.1000-0887.2014.11.008
ZHANG Xiao-hua, DENG Ji-heng. Research on the Meshless Solving Algorithm for 3D Steady ConvectionDiffusion Problems[J]. Applied Mathematics and Mechanics, 2014, 35(11): 1249-1258. doi: 10.3879/j.issn.1000-0887.2014.11.008
Citation: ZHANG Xiao-hua, DENG Ji-heng. Research on the Meshless Solving Algorithm for 3D Steady ConvectionDiffusion Problems[J]. Applied Mathematics and Mechanics, 2014, 35(11): 1249-1258. doi: 10.3879/j.issn.1000-0887.2014.11.008

三维稳态对流扩散问题的无网格求解算法研究

doi: 10.3879/j.issn.1000-0887.2014.11.008
基金项目: 国家自然科学基金(11102101;11171181);湖北省教育厅自然科学基金 (Q20111208)
详细信息
    作者简介:

    张小华(1980—),男,湖北宜昌人,副教授,博士(通讯作者. E-mail: dengjiheng@foxmail.com).

  • 中图分类号: TK124;TQ015.9

Research on the Meshless Solving Algorithm for 3D Steady ConvectionDiffusion Problems

Funds: The National Natural Science Foundation of China(11102101;11171181)
  • 摘要: 无网格法是一种不需要生成网格就可模拟复杂形状流场计算的流体力学问题求解算法.为了提高基于Galerkin弱积分形式的无网格方法求解三维稳态对流扩散问题的计算效率,提出了在空间离散上采用基于凸多面体节点影响域的无网格形函数,并通过选取适当节点影响半径因子避免节点搜索问题,同时减少系统刚度矩阵带宽.计算中当节点影响因子为1.01时,无网格方法的形函数近似具有插值特性且本质边界条件的施加与有限元一样简单.三维立方体区域的稳态对流扩散数值算例表明:在保证计算精度的同时,采用凸多面体节点影响域的无网格方法比传统无网格方法最高可节省计算时间42%.因此从计算效率和精度考虑,在运用无网格方法求解三维问题时建议采用凸多面体节点影响域的无网格方法.
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    [2] 张林. 基于多尺度无网格 Galerkin 方法的流动问题模拟[D]. 博士学位论文. 西安: 西北工业大学, 2010.(ZHANG Lin. The numerical simulation of flow problem based on multiscale element free Galerkin method[D]. PhD Thesis. Xi’an: North-Western Polytechnical University, 2010.(in Chinese))
    [3] 陶文铨, 吴学红, 戴艳俊. 无网格方法在流动和传热问题中的应用[J]. 中国电机工程学报, 2010,30(8): 1-8.(TAO Wen-quan, WU Xue-hong, DAI Yan-jun. Applications of meshless methods in fluid flow and heat transfer problems[J]. Proceedings of the CSEE,2010,30(8): 1-8.(in Chinese))
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    [10] ZHANG Lin, OUYANG Jie, ZHANG Xiao-hua. The variational multisclae element free Galerkin method for MHD flows at high Hartmann numbers[J]. Comput Phys Commun,2013,184(3): 1106-1118.
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  • 被引次数: 0
出版历程
  • 收稿日期:  2014-06-07
  • 修回日期:  2014-10-15
  • 刊出日期:  2014-11-18

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