Incompressibility of the Leray-α model for wall-bounded flows

M. van Reeuwijk, H. J. J. Jonker, K. Hanjalić

Physics of Fluids · 2006

Abstract

This study shows that the Leray-α model does not explicitly enforce a divergence-free field for the filtered velocity. While this condition is automatically satisfied in the absence of boundaries, bounded domains require extra attention. It is shown, both analytically and through simulations of Rayleigh–Bénard convection, that incompressibility of the filtered velocity field cannot be guaranteed in the current formulation. Several suggestions are made to restore the incompressibility of the filtered velocity, and it is shown that free-slip boundary conditions for the filtered velocity do guarantee incompressibility for the domain under consideration.