A New Stabilized Method for Quasi-Newtonian Flow

XIE Chun-mei; FENG Min-fu

doi:10.3879/j.issn.1000-0887.2010.09.004

Volume 31 Issue 9

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XIE Chun-mei, FENG Min-fu. A New Stabilized Method for Quasi-Newtonian Flow[J]. Applied Mathematics and Mechanics, 2010, 31(9): 1036-1049. doi: 10.3879/j.issn.1000-0887.2010.09.004

Citation:

XIE Chun-mei, FENG Min-fu. A New Stabilized Method for Quasi-Newtonian Flow[J]. Applied Mathematics and Mechanics, 2010, 31(9): 1036-1049. doi: 10.3879/j.issn.1000-0887.2010.09.004

Citation:

XIE Chun-mei, FENG Min-fu. A New Stabilized Method for Quasi-Newtonian Flow[J]. Applied Mathematics and Mechanics, 2010, 31(9): 1036-1049. doi: 10.3879/j.issn.1000-0887.2010.09.004

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A New Stabilized Method for Quasi-Newtonian Flow

doi: 10.3879/j.issn.1000-0887.2010.09.004

XIE Chun-mei¹,
FENG Min-fu^1,2

School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China;
School of Mathematics, Sichuan University, Chengdu 610064, P. R. China

Received Date: 1900-01-01
Rev Recd Date: 2010-07-02
Publish Date: 2010-09-15

Abstract

Abstract

For a generalized quasi-Newtonian flow,a new stabilized method focused on the low order velocity-pressure pairs((bi)linear/(bi)linear and(bi)linear/constant element)was presented.A development of pressure projection stabilized method was extended from Stokes problems to quasi-Newtonian flow problems.The theoretical framework developed herein yielded an estimate bound which measured the error in the approximation of the velocity in the W^1,r(Ω)norm and that of the pressure in the L^r'(Ω), (1/r+1/r'=1).The power-law model and the Carreau model were special ones of the quasi-Newtonian flow problem discussed.Moreover,a residual-based posterior bound was given.Finally,numerical experiments were presented to confirm our theoretical results.
- quasi-Newtonian,
- stabilized method,
- power law model,
- Carreau modle,
- residual-based posterior bound

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References(20)

References

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