A nonlinear weighted least-squares finite element method for the Carreau-Yasuda non-Newtonian model

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:432

Article

Lee, Hsueh-Chen

关键词: Weighted least-squares;    Nonlinear weight;    Non-Newtonian;    Carreau-Yasuda;    Shear-thinning;   

DOI  :  10.1016/j.jmaa.2015.07.012

来源: Elsevier

【 摘 要 】

We study a nonlinear weighted least-squares finite element method for the Navier-Stokes equations governing non-Newtonian fluid flows by using the Carreau-Yasuda model. The Carreau-Yasuda model is used to describe the shear-thinning behavior of blood. We prove that the least-squares approximation converges to linearized solutions of the non-Newtonian model at the optimal rate. By using continuous piecewise linear finite element spaces for all variables and by appropriately adjusting the nonlinear weighting function, we obtain optimal L-2-norm error convergence rates in all variables. Numerical results are given for a Carreau fluid in the 4-to-1 contraction problem, revealing the shear-thinning behavior. The physical parameter effects are also investigated. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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