Mathematical and numerical analysis of an alternative well-posed two-layer turbulence model (Q2781526)

We investigate the behavior of a two-layer \(k\)-\(\varepsilon \) turbulence model from the mathematical point of view, as this model is useful for the near-wall treatment in numerical simulations. First, we explain the difficulties inherent in the model. Then, we present a new variable \(\theta \) that enables the mathematical study. To handle the singularity of the turbulent viscosity on the wall boundary, we consider an alternative version of the original equation. We show that some physical aspects of the model are preserved by the new formulation. Finally, we are interested in the Navier-Stokes equations coupled with the modified turbulence model and we show that the alternative model may be preferred to the original one, because of its good properties (existence of a solution of the coupled problems).