J.S. Travelho; Filho, N.P.; H.F. Campos Velho; A.V. Moura; M. Dreux (1995): A Finite Difference Method Applied to the $\kappa$-$\epsilon$-$\gamma$ Turbulence Model in a Constant-Density Jet in Still Air, Italian-Latinamerican Conference on Applied and Industrial Mathematics (ITLA-95), pp. 36.

Abstract: This work shows an application of the $\kappa$-$\epsilon$-$\gamma$ turbulence model of Cho and Chung using a finite-difference method. The $\kappa$-$\epsilon$-$\gamma$ model is similar to the standard $\kappa$-$\epsilon$ model with an transport equation for the intermittency $\gamma$. This intermittency is used in the turbulent viscosity calculation. These authors show the equations for this model but mention problems related to its application in a finite difference scheme, saying that an apraisal of the model with finite difference was not possible due errors introduced by this kind of discretization. With the aid of Scientific Visualization was possible to localize the major sources of errors in a implementation of this model together with a finite difference scheme. Increasing the number of nodes in the mesh this problem was circumvented and it was possible to obtained results very close to the experimental ones. The finite difference scheme used in this work is the one described by Patankar and Spalding. It is a parabolic model with the stream function as one of the coordinates. The results generated by this work shows a good agreement with experimental data.