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流变计算的高性能有限元收敛性分析

侯磊 孙先艳 赵俊杰 李涵灵

侯磊, 孙先艳, 赵俊杰, 李涵灵. 流变计算的高性能有限元收敛性分析[J]. 应用数学和力学, 2014, 35(4): 412-422. doi: 10.3879/j.issn.1000-0887.2014.04.007
引用本文: 侯磊, 孙先艳, 赵俊杰, 李涵灵. 流变计算的高性能有限元收敛性分析[J]. 应用数学和力学, 2014, 35(4): 412-422. doi: 10.3879/j.issn.1000-0887.2014.04.007
HOU Lei, SUN Xian-yan, ZHAO Jun-jie, LI Han-ling. Convergence of Finite Element Method in Rheology[J]. Applied Mathematics and Mechanics, 2014, 35(4): 412-422. doi: 10.3879/j.issn.1000-0887.2014.04.007
Citation: HOU Lei, SUN Xian-yan, ZHAO Jun-jie, LI Han-ling. Convergence of Finite Element Method in Rheology[J]. Applied Mathematics and Mechanics, 2014, 35(4): 412-422. doi: 10.3879/j.issn.1000-0887.2014.04.007

流变计算的高性能有限元收敛性分析

doi: 10.3879/j.issn.1000-0887.2014.04.007
基金项目: 国家自然科学基金(11271247)
详细信息
    作者简介:

    侯磊(1957—),男,上海人,教授,博士,博士生导师(通讯作者. Tel: +86-21-66129636;E-mail: houlei@shu.edu.cn)

  • 中图分类号: O357.1

Convergence of Finite Element Method in Rheology

Funds: The National Natural Science Foundation of China(11271247)
  • 摘要: 文中研究非Newton(牛顿)流体流变问题的混合型双曲抛物一阶偏微分方程的收敛性,采用耦合的偏微分方程组(Cauchy流体方程、P-T/T应力方程),模拟自由表面元或由过度拉伸元素产生的流域.使用半离散有限元方法进行求解,对于含有时间变量的耦合方程,在空间上用有限元法,利用三线性泛函来解决偏微分方程组的非线性;在时间上用Euler(欧拉)格式,得出方程组的收敛精度可达到O(h2+Δt).通过高性能计算的预估计和后估计得到方程的数值结果,并显示网格变形的大小.
  • [1] HOU Lei, Nassehi V. Evaluation of stress-effective flow in rubber mixing[J].Nonlinear Analysis,2001,47(3): 1809-1820.
    [2] HOU Lei, Paris R B, Wood A D. The resistive interchange mode in the presence of equilibrium flow[J].Physics of Plasmas,1996,3(2): 473-481.
    [3] 林群, 严宁宁. 关于Maxwell方程混合元方法的超收敛[J]. 工程数学学报, 1996,13(supp): 1-10, 66.(LIN Qun, YAN Ning-ning. Superconvergence of mixed methods for the Maxwell’s equations[J].Journal of Engineering Mathematics,1996,13(supp): 1-10, 66.(in Chinese))
    [4] Van Schaftingen J J, Crochet M J. A comparison of mixed methods for solving the flow of a Maxwell fluid[J].International Journal for Numerical Methods in Fluids,1984,4(11): 1065-1081.
    [5] LIN Jia-fu, LIN Qun. Global superconvergence of the mixed finite element methods for 2-D Maxwell equations[J].Journal of Computational Mathematics,2003,21(5): 637-646.
    [6] HOU Lei, ZHAO Jun-jie, LI Han-ling. Finite element convergence analysis of two-scale non-Newtonian flow problems[J].Advanced Materials Research, 2013,718/720: 1723-1728.
    [7] HOU Lei, CAI Li. Nonlinear property of the visco-elastic-plastic material in the impact problem[J].Journal of Shanghai University(English Edition),2009,13(1): 23-28.
    [8] HOU Lei, LIN De-zhi, WANG Bin, LI Han-ling, QIU Lin. Computational modelling on the contact interface with boundary-layer approach[C]// Proceedings of the World Congress on Engineering. VolI. London, UK, 2011: 39-44.
    [9] Sugeng F, Phan-Thien N, Tanner R I. A study of non-isothermal non-Newtonian extrudate swell by a mixed boundary element and finite element method[J].Journal of Rheology,1987,31(1): 37-58.
    [10] 林群, 林甲富. 二维Maxwell方程组的混合有限元高精度近似[J]. 数学物理学报, 2003,23A(4): 499-503.(LIN Qun, LIN Jia-fu. High accuracy approximation of mixed finite element for 2-d Maxwell equations[J].Acta Mathematica Scientia,2003,23A(4): 499-503.(in Chinese))
    [11] HOU Lei, Harwood R. Nonlinear properties in Newtonian and non-Newtonian equations[J].Nonlinear Analysis,1997,30(4): 2497-2505.
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出版历程
  • 收稿日期:  2013-10-18
  • 修回日期:  2014-03-13
  • 刊出日期:  2014-04-15

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