A spectral/hp least-squares finite element analysis of the Carreau-Yasuda fluids

作者：Kim Namhee; Reddy J N^*

来源：International Journal for Numerical Methods in Fluids, 2016, 82(9): 541-566.

DOI：10.1002/fld.4230

• least-squares finite element model
• spectral
• hp elements
• non-Newtonian fluid
• the Carreau-Yasuda model
• Kovasznay flow
• backward-facing step flow
• lid-driven square cavity flow

A least-squares finite element model with spectral/hp approximations was developed for steady, two-dimensional flows of non-Newtonian fluids obeying the Carreau-Yasuda constitutive model. The finite element model consists of velocity, pressure, and stress fields as independent variables (hence, called a mixed model). Least-squares models offer an alternative variational setting to the conventional weak-form Galerkin models for the Navier-Stokes equations, and no compatibility conditions on the approximation spaces used for the velocity, pressure, and stress fields are necessary when the polynomial order (p) used is sufficiently high (say, p > 3, as determined numerically). Also, the use of the spectral/hp elements in conjunction with the least-squares formulation with high p alleviates various forms of locking, which often appear in low-order least-squares finite element models for incompressible viscous fluids, and accurate results can be obtained with exponential convergence. To verify and validate, benchmark problems of Kovasznay flow, backward-facing step flow, and lid-driven square cavity flow are used. Then the effect of different parameters of the Carreau-Yasuda constitutive model on the flow characteristics is studied parametrically.

• 出版日期2016-11-30