Well-posedness of the slip wall boundary conditions for the LES equations

A Robin boundary condition admitting instantaneous and local transpiration (but no net transpiration) has been shown to be a suitable boundary condition for wall-modeled large eddy simulation. Well-posedness of these boundary conditions is analyzed through the consideration of the global kinetic energy and entropy evolution equations for the incompressible and compressible LES governing equations, respectively. Most existing analysis of well-posedness of wall boundary conditions consider Dirichlet boundary conditions for the wall normal velocity (no penetration) for the filtered or unfiltered Navier-Stokes equations. The present analysis seeks to identify under which conditions a bounded solution can be expected, which is particularly valuable when the slip lengths are dynamically computed. Preliminary computational results from the LES of a plane channel flow are presented to support these theoretical claims. The global kinetic energy in the domain is shown to grow or decay in time, depending on the procedure for enforcing the slip wall boundary condition.