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线性化粘弹流体流的自适应亏量校正算法研究
  • ISSN号：1005-3085
  • 期刊名称：《工程数学学报》
  • 时间：0
  • 分类：O241[理学—计算数学;理学—数学]
  • 作者机构：[1]河南科技大学数学与统计学院,洛阳471023, [2]南京大学数学系,南京210093, [3]西安交通大学数学与统计学院,西安710049
  • 相关基金：The National Natural Science Foundation of China （11171269; 11401074）; the Ph.D. Program Foundation of Ministry of Education of China （20110201110027）; the China Postdoctoral Science Foundation （2013M531311）; the Research Fund of Educational Commission of Henan Province of China （14B110020; 14B110021; 14B110025）; the Henan Scientific and Technological Research Project （132102310309）; the Doctoral Foundation of Henan University of Science and Technology （09001625）; the Science Foundation for Cultivating Innovation Ability of Henan University of Science and Technology （2014ZCX009）; the Youth Scientific Foundation of Henan University of Science and Technology （2012QN029）.
作者： 张运章[1,2], 魏红波[3], 侯延仁[3]
关键词： 线性化粘弹流体流, 有限元方法, 自适应预估校正算法, 后验误差估计, linearized viscoelastic fluid flow, finite element method, adaptive defect correction method, posteriori error estimate
中文摘要：

本文研究粘弹性非牛顿流体的数值计算问题．粘弹性非牛顿流体是介于流体和固体之间的，具有复杂本构关系的物质．由于该问题极其复杂，它的数值模拟非常困难．本文将预估校正方法和自适应有限元方法结合起来研究了线性化粘弹流体流．理论上得到了自适应预估校正方法的可依赖后验误差估计．最后给出一些数值试验验证了自适应预估校正方法对于线性化粘弹流体流的有效性．本文为进一步研究更复杂的粘弹性非牛顿流体奠定了基础．

英文摘要：

This paper is concerned with some numerical computation on viscoelastic non- Newtonian fluids. Viscoelastic non-Newtonian fluids can be viewed as the intermediate states between the fluids and the solids. As viscoelastic non-Newtonian fluids is complex, it is very difficult to numerically solve the problem. In this paper, we combine the defect correction method and the adaptive method to study linearized viscoelastic fluid flow. A reliable a posteriori error estimate is derived for the adaptive defect correction method. Numerical experiments are provided which ill-ustrate the utility of the resulting adaptive defect correction method for linearized viscoelastic fluid flow. The obtained results can be viewed as the basis for further research on more complex viscoelastic non-Newtonian fluids.

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期刊信息
  • 《工程数学学报》
  • 北大核心期刊（2011版）
  • 主管单位:教育部
  • 主办单位:西安交通大学
  • 主编：李大潜
  • 地址：西宁市咸宁西路28号西安交通大学数学与统计学院
  • 邮编：710049
  • 邮箱：jgsx@mail.xjtu.edu.cn
  • 电话：029-82667877
  • 国际标准刊号：ISSN：1005-3085
  • 国内统一刊号：ISSN：61-1269/O1
  • 邮发代号:
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  • 被引量:6741