A least-squares finite element method for steady flows across an unconfined square cylinder placed symmetrically in a plane channel

Abstract

This paper develops a least-squares finite element method (LSFEM) for non-Newtonian flows of power-law fluid across an unconfined square cylinder at two inclination angles, placed symmetrically in a two-dimensional channel. We used Newton's method to linearize the equation of motion and employed the least-squares approach with systematic mesh refinements to flow past the square cylinder. The LSFEM offers a direct approximation of the extra stress tensor components, a symmetric positive definite system, and the openness of choosing finite element spaces. We proved that the least-squares approximation converges to linearized solutions of non-Newtonian fluid flows. We demonstrated that the numerical results using low-order basis functions agree with the theoretical estimates and presented the effects of different physical parameters on the physical attributes of the power-law model at a low Reynolds number, such as drag coefficients, viscosity, and velocity. These results agree with others published in the literature. Hence, the LSFEM in non-Newtonian fluid simulations can accomplish the identification of shear-thinning and shear-thickening characteristics.