A Numerical Method for Simulation of Incompressible Three-Dimensional Newtonian and Non-Newtonian Flows

Abstract

Three-dimensional Newtonian and non-Newtonian flows are found in numerous engineering applications. Simulation of this class of problems requires robust mathematical and computational modeling. The main goal of this article is to propose a unified numerical methodology for solving three-dimensional, laminar, incompressible Newtonian and non-Newtonian steady flows. A second-order, fully implicit finite-difference approximation is used to discretize the governing equations in a collocated mesh, in which Jacobian matrices are derived to account for distinct constitutive relations for Newtonian and non-Newtonian fluids. The strategy also uses a Euler implicit pseudo-transient time stepping aiming at steady-state solutions. Examples illustrating Newtonian and non-Newtonian (polymer melts) fluid flow in 3-D geometries are discussed.

Acknowledgments

P. S. B. Zdanski acknowledges the financial support and scholarship provided by the by CNPq (National Council for Scientific and Technological Development) under grants 471619/2009-4 and 301206/2009-0.