Finite element approximations for quasi-Newtonian flows employing a multi-field GLS method

Abstract

This article concerns stabilized finite element approximations for flow-type sensitive fluid flows. A quasi-Newtonian model, based on a kinematic parameter of flow classification and shear and extensional viscosities, is used to represent the fluid behavior from pure shear up to pure extension. The flow governing equations are approximated by a multi-field Galerkin least-squares (GLS) method, in terms of strain rate, pressure and velocity (D-p-u). This method, which may be viewed as an extension of the formulation for constant viscosity fluids introduced by Behr et al. (Comput Methods Appl Mech 104:31---48, 1993), allows the use of combinations of simple Lagrangian finite element interpolations. Mild Weissenberg flows of quasi-Newtonian fluids--using Carreau viscosities with power-law indexes varying from 0.2 to 2.5--are carried out through a four-to-one planar contraction. The performed physical analysis reveals that the GLS method provides a suitable approximation for the problem and the results are in accordance with the related literature.