Numerical Simulation of the Incompressible Navier–stokes Equations

Abstract

A scheme for the numerical simulation of incompressible flows is presented. The modeling equations are written in conservation law form. The algorithm, written in a delta form, is very robust without resorting to any degree of relaxation. The well-known cumbersome numerical implementation related to staggered grids is totally removed. The scheme is second-order-accurate in space and first-order in time. An important novelty is the separation of the pressure terms in the physical equations in a pressure flux, facilitating the tackling of different fluids. The algorithm has been applied to laminar and turbulent flows. The results are truly encouraging.

A fully implicit finite difference scheme for velocity and temperature coupled solutions of polymer melt flow

“…The numerical scheme presented in this work is an extension of the techniques originally conceived for incompressible Newtonian flows [3]. A fully implicit solution, central discretization for both convective and diffusive terms, collocated meshes and artificial dissipation to control spurious pressure modes are the main features of the method.…”

“…In addition, development of computational techniques for non-Newtonian fluids, in special polymer melt flows, has gained momentum in recent years when new approaches based on viscoelastic and generalized Newtonian assumptions have been proposed. The present work extends the techniques originally conceived for incompressible Newtonian fluid flows [3] to include viscous dissipation effects and a new shear 286 M. VAZ JR AND P. S. B. ZDANSKI rate and temperature-dependent constitutive relation. Furthermore, the solution procedure has also been redesigned in order to maintain the fully implicit character of the original algorithm.…”

Numerical Simulation of the Incompressible Turbulent Flow of a Binary Mixture of Air-Water Vapor: Applications in Drying Process

“…The solution procedure follows a pseudo-transient march in time, aiming at the steady-state solution. The present work constitututes an extension of the author's methodology (Zdanski et al, 2004;Zdanski et al, 2008;Zdanski and Vaz Jr., 2011) for solving turbulent flows of binary mixtures. The main general steps of the present scheme are given in sequence.…”

“…The complete procedure to control the magnitude of the artificial smoothing terms is described by Zdanski et al (2004).…”

“…The numerical scheme applied by the authors was originally proposed for solving turbulent Newtonian flows (Zdanski et al 2004). The present methodology was also applied successfully to solve non-Newtonian polymer melt flows inside channels (Zdanski et al, 2008;Zdanski and Vaz Jr., 2011).…”