Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 12741, 26 pages
Research Article

Incompressible Turbulent Flow Simulation Using the κ-ɛ Model and Upwind Schemes

V. G. Ferreira,1 A. C. Brandi,1 F. A. Kurokawa,1 P. Seleghim Jr.,2 A. Castelo,1 and J. A. Cuminato1

1Departamento de Matemática Aplicada e Estatística, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo (USP), São Carlos Caixa Postal 668, CEP 13560-970, SP, Brazil
2Departamento de Engenharia Mecânica, Escola de Engenharia de São Carlos, Universidade de São Paulo (USP), São Carlos Caixa Postal 359, CEP 13566-590, SP, Brazil

Received 30 November 2006; Accepted 25 March 2007

Academic Editor: José Manoel Balthazar

Copyright © 2007 V. G. Ferreira et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In the computation of turbulent flows via turbulence modeling, the treatment of the convective terms is a key issue. In the present work, we present a numerical technique for simulating two-dimensional incompressible turbulent flows. In particular, the performance of the high Reynolds κ-ɛ model and a new high-order upwind scheme (adaptative QUICKEST by Kaibara et al. (2005)) is assessed for 2D confined and free-surface incompressible turbulent flows. The model equations are solved with the fractional-step projection method in primitive variables. Solutions are obtained by using an adaptation of the front tracking GENSMAC (Tomé and McKee (1994)) methodology for calculating fluid flows at high Reynolds numbers. The calculations are performed by using the 2D version of the Freeflow simulation system (Castello et al. (2000)). A specific way of implementing wall functions is also tested and assessed. The numerical procedure is tested by solving three fluid flow problems, namely, turbulent flow over a backward-facing step, turbulent boundary layer over a flat plate under zero-pressure gradients, and a turbulent free jet impinging onto a flat surface. The numerical method is then applied to solve the flow of a horizontal jet penetrating a quiescent fluid from an entry port beneath the free surface.