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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (6): 927-940.doi: 10.3969/j.issn.1005-3085.2015.06.014

• • 上一篇    下一篇

线性化粘弹流体流的自适应亏量校正算法研究(英)

张运章1,2,   魏红波3,   侯延仁3   

  1. 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
  • 收稿日期:2013-09-17 接受日期:2014-12-02 出版日期:2015-12-15 发布日期:2016-02-15
  • 基金资助:
    国家自然科学基金 (11171269; 11401074)；教育部博士点基金 (20110201110027)；中国博士后科学基金 (2013M531311)；河南省教委科研基金 (14B110020; 14B110021; 14B110025); 河南省科技攻关项目 (132102310309)；河南科技大学博士基金 (09001625)；河南科技大学创新能力培养科学基金 (2014ZCX009)；河南科技大学青年科学基金 (2012QN029).

Adaptive Defect Correction for Linearized Viscoelastic Flow

ZHANG Yun-zhang1,2,   WEI Hong-bo3,   HOU Yan-ren3   

  1. 1- School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023
    2- Department of Mathematics, Nanjing University, Nanjing 210093
    3- School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049
  • Received:2013-09-17 Accepted:2014-12-02 Online:2015-12-15 Published:2016-02-15
  • Supported by:
    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).

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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．

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

Abstract:

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.

Key words: linearized viscoelastic fluid flow, finite element method, adaptive defect correction method, posteriori error estimate

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