Least-squares finite element analysis of flow of a generalized Newtonian fluid past a circular cylinder

ABSTRACT

A mixed least-squares finite element model (LSFEM) with spectral/hp approximations is developed for the analysis of steady, two-dimensional flows of generalized Newtonian fluids obeying the Carreau–Yasuda constitutive model. The finite element model (FEM) is composed of velocity, pressure, and stress fields as independent variables (therefore, called a mixed model). FEMs based on least-squares formulations are considered an alternative variational setting to the conventional weak-form Galerkin models for the Navier–Stokes equations, and no compatibility conditions on the approximation spaces are needed for the velocity, pressure, and stress fields if the polynomial order (p) is sufficiently high (say, p > 3, as determined numerically). In addition, applying high-order spectral/hp approximation functions to the least-squares formulation avoids various forms of locking that often occur in low-order LSFEMs for incompressible viscous fluids, and accurate results can be obtained with exponential convergence. The benchmark problem of the flow past a circular cylinder is solved to verify and validate the model. Then, a parametric study is performed to examine the effect of change in parameters of the Carreau–Yasuda model on the flow past a circular cylinder.

KEYWORDS:

• Least-squares finite element model
• spectral/hp approximation
• non-Newtonian fluid
• Carreau–Yasuda model
• flow past a circular cylinder

Additional information

Funding

The authors gratefully acknowledge the support from the Department of Defense (DoD) Award: SC130156 (W81XWH-14-1-0600) as well as the Oscar S. Wyatt Endowed Chair.