Positivity Preservation and Adaptive Solution for the k-? Model of Turbulence

Abstract

A simple change of dependent variables that guarantees positivity of turbulence variables in numerical simulation codes is presented. The approach consists of solving for the natural logarithm of the turbulence variables, which are known to be strictly positive. The approach is valid for any numerical scheme, be it finite difference, a finite volume, or a finite element method. The work focuses on the advantages of the proposed change of dependent variables within the framework of an adaptive finite element method. The turbulence equations in logarithmic variables are presented for the standard κ-e model. Error estimation and mesh adaptation procedures are described. The formulation is validated on a shear layer case for which an analytical solution is available. This provides a framework for rigorous comparison of the proposed approach with the standard solution technique, which makes use of k and e as dependent variables. The approach is then applied to solve turbulent flow over a NACA0012 airfoil for which experimental measurements are available. The proposed procedure results in a robust adaptive algorithm. Improved predictions of turbulence variables are obtained using the proposed formulation