P-Version least squares finite element formulation for three-dimensional, isothermal, incompressible, non-Newtonian fluid flow

Abstract

A p-version least squares finite element formulation has been presented for the dimensionless form of the Navier-Stokes equations for incompressible, isothermal, non-Newtonian fluid flow. The characteristic kinetic energy is used to non-dimensionalize the stresses. The viscosity of the fluid can be described by the power law or Carreau-Yasuda model. The Navier-Stokes equations are recast into a set of first-order partial differential equations using stresses as auxiliary variables. This permits the use of C 0 approximation functions for both primary and auxiliary variables. The Newton's method with a line search is used to find a solution vector which satisfies the necessary and the sufficient conditions resulting from the least squares minimization procedure. Numerical examples are presented to demonstrate the p-convergence characteristics, convenience of simple and coarse models and the accuracy of the solution. Numerical results are compared with the analytical solutions as well as with those reported in the literature.