SNENS III - Numerical Solution of Navier-Stokes Equations: Three-dimensional Flows

Abstract

The numerical solution of viscous fluid flow possessing free surfaces has become possible due to the recent advances in computer technology and the development of new numerical techniques for solving partial diferencial equations. Many practical problems can be modelled as free surface problems, for instance, injection moulding, thin film flows in the condensing process and molten iron and steel. Moreover, many industrial problems involve transient fluid flow in complex domains. For instance, in the food industry a number of problems involve the filling of complex shaped containers. There is therefore a great interest in developing numerical techniques for tackling these problems. Indeed, in the past 5 years, the applied mathematics group at ICMC-USP de São Carlos, has been working in the development of an environmental shell for handling three-dimensional flows called Freeflow-3D. Freeflow-3D has been designed in three distinct and independent modules: a modeller module (Modfiow-3D), a simulator module(Simflow-3D) and a visualization module (Visflow-3D). Modflow-3D provides a friendly interface for specifying the domain and the initial fluid. It includes elements such as the containers, the injection nozzle(s) and the initial values of velocity and pressure of the fluid. This module is fundamental for the easy starting of Freeflow-3D. Simflow-3D is the central part of Freeflow-3D as it contains the computational techniques of CFD. It implements the discretization of the governing equations and boundary conditions. Visflow-3D is an interactive system for the visualization of the output of Simflow-3D using visualization techniques. It employs several visualization algorithms using the latest developments in computer graphics. Freeflow-3D is fully operational and has been employed to simulate a number of free surface problems in three-dimensions (see the numerical examples presented in the research plan). The aim of this project is to develop Freeflow-3D further so that it can handie more general fluid dynamic problems. The problems to be tackled are: simulation of free surface flows in complex domains such as that of filling containers having complex shaped geometries (e.g. containers employed in the chemical industries)and modelling of complex shaped nozzles; development of a numerical method for solving viscoelastic fluid flows (e.g. Oldroyd-B fluid) as well as flows of generalized fluids (e.g. power-law and Cross model fluids). Inclusion of surface tension into Freeflow-3D. This will allow Freeflow-3D to simulate flows under surface tension forces such as drops, hydraulic jump, etc; implementation of a high order method for approximating the non-linear terms of the Navier-Stokes equations. We intend to investigate a high order upwind scheme (e.g.SMART, VONOS) to approximate the convective terms of the Navier-Stokes equations. This will allow Freeflow-3D to simulate high Reynolds number flows; simulation of turbulent flows. We intend to include a turbulent model into Freeflow-3D. First we will implement the k - e into the two-dimensional GENSMAC code and the next end Freefiow-3D to deal with three-dimensional turbulent flows. (AU)