On reformulating the erm-based second-moment closure towards a more robust turbulence model

The present study considers a reformulation of the Durbin's (1993) ERM-based second-moment closure model aiming at reduction of the numerical stiffness originating from the wall boundary conditions. The reformulation performed represents an analogy to the procedure Hanjalic et al. (2004) proposed when deriving the eddy-viscosity-based ζ − f model. The presently reformulated model alternatively solves the transport equations for the ratio of the Reynolds stress components to turbulent kinetic energy ζ_ij = uiu_j/k, instead of equations governing the Reynolds stress tensor. It is believed that the boundary conditions of the newly derived elliptic relaxation equations will contribute to the numerical robustness of the model with respect to the immediate wall vicinity. Another advantage, analogously to the Hanjalic's et al. ζ − f model, is the appearance of the Reynolds stress production rate (representing an exact formulation) in the ζ_ij equations instead of dissipation rate ε (originating from the corresponding model equation). Application of the present model formulation to a plane channel flow in a range of Reynolds numbers up to Re_τ = 2003 results in a good agreement with available DNS database.