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3-D least-squares finite element analysis of flows of generalized Newtonian fluids

机译:推广牛顿流体流量的三维最小二乘性有限元分析

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摘要

A mixed least-squares finite element model with spectral/hp approximations was developed to analyze three-dimensional, steady, and incompressible flows of generalized Newtonian fluids. The Carreau-Yasuda constitutive model was used for viscosity model. Velocity, pressure, and stress are the field variables of the finite element model (hence, called a mixed model). The least-squares formulation offers a variational setting for the Navier-Stokes equations; hence no compatibility of the approximation spaces used for the velocity, pressure, and stress fields is imposed if the polynomial order is sufficiently high. Also, using high-order spectral/hp elements in the least-squares formulation for the Navier-Stokes equations alleviates various forms of locking and accurate results can be obtained with exponential convergence. To verify the present formulation and computational module, the method of manufactured solutions and two different benchmark problems (namely, lid-driven cavity flow and backward-facing step flow) are used. Then the effect of different parameters of the Carreau-Yasuda model on the flow behavior is studied.
机译:开发了一种具有光谱/ HP近似的混合最小二乘有限元模型,以分析三维,稳定和不可压缩的广义牛顿流体流动。 Carreau-Yasuda本构模型用于粘度模型。速度,压力和应力是有限元模型的场变量(因此,称为混合模型)。最小二乘配方为Navier-Stokes方程提供了变化设置;因此,如果多项式顺序足够高,则不施加用于速度,压力和应力场的近似空间的兼容性。此外,在Navier-Stokes方程中使用的高阶频谱/ HP元件用于Navier-Stokes方程,可以通过指数收敛获得各种形式的锁定和准确的结果。为了验证本制定和计算模块,使用制造解决方案的方法和两个不同的基准问题(即,盖子驱动的腔流量和后向步骤流程)。然后,研究了Carreau-Yasuda模型对流动行为的不同参数的影响。

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