On a one-equation turbulent model with feedbacks

Abstract

A one-equation turbulent model is derived in this work on the basis of the approach used for the k-epsilon model. The novelty of the model consists in the consideration of a general feedback forces field in the momentum equation and a rather general turbulent dissipation function in the equation for the turbulent kinetic energy. For the steady-state associated boundary value problem, we prove the uniqueness of weak solutions under monotonous conditions on the feedbacks and smallness conditions on the solutions to the problem. We also discuss the existence of weak solutions and issues related with the higher integrability of the solutions gradients.