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

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

¹上海大学理学院数学系, 上海 200444;²上海交通大学上海高校计算科学E研究院, 上海 200030

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
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- 被引次数: 0
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

Convergence of Finite Element Method in Rheology

¹Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P.R.China;²Computational Science E-Institute of Shanghai Universities, Shanghai Jiao Tong University, Shanghai 200030, P.R.China

Funds: The National Natural Science Foundation of China（11271247）

摘要

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.
- 非Newton流体 /
- 半离散有限元 /
- 耦合方程 /
- 收敛
Abstract: Convergence of the first-order mixed-type hyperbolic parabola partial differential equations in non-Newtonian fluid problems was studied. The coupling partial differential equations (Cauchy fluid equation, P-T/T stress equation) were used to simulate the flow zone generated by the free surface elements or excessively tensile elements. The semi-discrete finite element method was applied to solve these equations coupling with time. The finite element method was used in space. The trilinear functional was employed to solve the nonlinear problems of partial differential equations. In the time domain the Euler scheme was adopted. The convergence order of the equation set reached O(h2+Δt). Numerical results of the equations were obtained through priori and posteriori error estimation of high performance computation. And the deformed sizes of the grids were presented.
- non-Newtonian fluid /
- semi-discrete finite element /
- coupling equations /
- convergence

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参考文献(11)

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