Least‐squares finite element analysis of three‐dimensional natural convection of generalized Newtonian fluids,International Journal for Numerical Methods in Fluids

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Least‐squares finite element analysis of three‐dimensional natural convection of generalized Newtonian fluids
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2020-10-11 , DOI: 10.1002/fld.4929
Namhee Kim ₁ , J. N. Reddy ₂

Affiliation

A mixed least‐squares finite element model with spectral/hp approximations was developed to analyze a three‐dimensional natural convection of non‐Newtonian fluid, which obeys the Carreau–Yasuda constitutive model. The finite element model consists of velocity, pressure, stress, temperature, and heat flux as the field variables. The least‐squares formulation provides a variational framework for the Navier–Stokes equations and no compatibility of the approximation spaces for field variables is imposed. Also, the use of spectral/hp elements in conjunction with the least‐squares formulation alleviates various forms of locking which often appear in low‐order least‐squares finite element models for incompressible viscous flows and yields accurate results with exponential convergence. To verify and validate the code for Newtonian fluids, the current results are compared with the numerical and experimental results in the literature. Then, the parametric effects of the Carreau–Yasuda model on the flow characteristics are studied.

中文翻译：

广义牛顿流体三维自然对流的最小二乘有限元分析

建立了一个混合光谱/马力近似的最小二乘有限元模型，以分析非牛顿流体的三维自然对流，它遵循Carreau–Yasuda本构模型。有限元模型由速度，压力，应力，温度和热通量组成，它们是场变量。最小二乘公式为Navier–Stokes方程提供了一个变分框架，并且不对字段变量施加近似空间的兼容性。另外，使用光谱/马力元素与最小二乘公式结合可缓解各种形式的锁定，这些形式通常出现在不可压缩粘性流的低阶最小二乘有限元模型中，并产生具有指数收敛性的精确结果。为了验证和验证牛顿流体的代码，将当前结果与文献中的数值和实验结果进行了比较。然后，研究了Carreau-Yasuda模型对流动特性的参数影响。

更新日期：2020-10-11

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