The dynamic procedure for closure relations in the equation of filtered concentration of suspended solid particles

In this paper, a LES model, developed for the simulation of turbulent channel flow and lid driven cavity (in which the generalized SGS stress tensor is related to the SGS turbulent kinetic energy and SGS viscous dissipation), will be extended to include the simulation of the re-suspension of solid particles from an erodible bed. The solid particle concentration fields are simulated by numerical integration of the spatially filtered equation of concentration. In this equation the first order tensor (produced by the second order generalized central moment relative to the correlation between velocity and concentration) is related to the gradient of the resolved concentration by means a second order tensor; the coefficient that is present in this closure relation is calculated by a dynamic procedure. The boundary conditions, for the numerical integration of the filtered equation of the concentration, in proximity to the bottom are defined by the value of the unsteady Reference Concentration Cr. The unsteady reference concentration Cr is imposed, dynamically, on the plane that is placed immediately above the viscous sublayer, inside the buffer layer.