A UNIFIED FINITE-ELEMENT ALGORITHM FOR 2-EQUATION MODELS OF TURBULENCE

This paper presents a simple change of dependent variables for turbule nce quantities that achieves two goals: the resulting formulation pres erves positivity of all turbulence variables; and leads naturally to a simple algorithm applicable to all two-equation models of turbulence. It is also a useful means for comparing the structure of different tu rbulence models. The approach consists in solving for the natural loga rithm of the turbulence variables. The methodology is illustrated by a pplying it to three popular models: the standard k-epsilon model; the k-tau model of Speziale; and the k-omega model of Wilcox. When logarit hmic variables are used, transport equations for one model are obtaine d by adding or subtracting those from another model and by using the s imple relationships that exist between the logarithms of k, epsilon, o mega and tau. An existing adaptive finite element algorithm developed for the logarithmic form of the k-epsilon model is applied to the othe r models without any change. The formulation is verified on a shear la yer possessing a closed form solution. The approach is then applied to turbulent Row over backward facing step for which measurements are av ailable. Computations show that solutions of controlled accuracy can b e achieved using the same solution algorithm for all models thus openi ng the way to systematic comparison studies. (C) 1998 Elsevier Science Ltd. All rights reserved.