In this article, we wish to investigate the behavior of a two-layer $k-\epsilon$ 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. Due to a problem of definition of the turbulent viscosity on the wall boundary, we consider an alternative version of the original equation. We show that some physical aspects...

In this article, we wish to investigate the behavior of a two-layer k - ε 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 θ that enables the mathematical study. Due to a problem of definition of the turbulent viscosity on the wall boundary, we consider an alternative version of the original equation. We show that some physical...

In this paper, we establish the large-data and long-time existence of a suitable weak solution to an initial and boundary value problem driven by a system of partial differential equations consisting of the Navier-Stokes equations with the viscosity $\nu$ polynomially increasing with a scalar quantity $k$ that evolves according to an evolutionary convection diffusion equation with the right hand side $\nu \left(k\right)|𝖣\left(\overrightarrow{v}\right){|}^2$ that is merely $L^1$-integrable over space and time. We also formulate a conjecture concerning regularity...

2D shallow water equations with depth-averaged k−ε model is considered. A meshless method based on multiquadric radial basis functions is described. This methods is based on the collocation formulation and does not require the generation of a grid and any integral evaluation. The application of this method to a flow in horizontal channel, taken as an experimental device, is presented. The results of computations are compared with experimental data...