A numerical methodology for simulation of non-Newtonian viscoelastic flows

The non-Newtonian fluids presenting viscoelastic flow behavior are found in many engineering applications. The development of a new numerical scheme for solution of this class of problems is the main goal of the present work. The proposed methodology adopts a second-order fully implicit finite difference approximation to discretize the convection and diffusion terms in the governing equations. Besides, the discretization is accomplished in a collocated mesh arrangement being used an Euler implicit pseudo-transient march in time aiming at steady-state solutions. Finally, it is worth mentioning that under-relaxation parameters are not needed, and the odd-even decoupling problem is avoided using artificial dissipations terms that are externally controlled by the user. The examples illustrating the application of the present method are: the non-Newtonian flows of viscoelastic materials in a plane channel and in a lid-driven cavity. The validation/verification performed indicates that the results are truly encouraging.