EXISTENCE AND POSITIVITY RESULTS FOR THE φ−θ AND A MODIFIED k−ε TWO-EQUATIONTURBULENCE MODELS

Abstract

In this work, we consider the k−ε two-equation turbulence model from the point of view of mathematical and numerical analysis. We introduce a new equivalent two-equation model based on a new set of variables. In the first part, we study this model with a constant eddy viscosity. In this model, the coupling between the equations is done only through the right-hand side. In the second part, we consider the complete model with a nonlinear viscosity. Finally, the impact of this new change of variables on the numerical computations with the k−ε model is shown and a robust algorithm which preserves the positivity of the variables is given.