I am trying to develop a code to solve NS equations using LES. If I take a fixed eddy viscosity, the total mass is conserved and If I use Smagorinsky model, then the total mass conservation is not achieved. The total mass starts decreasing. I am using finite volume method with velocities on the walls and concentrations, pressure and eddy viscosity in the center of the cell. I am using QUICKEST for advection and central differeence scheme for diffusion. If anyone please help and give some suggestions !! Thanks, Sas

Check to see if you are using QUICKEST correctly - what goes out of the left cell must enter the right cell. This is most likely your problem.

Also, how do you enforce mass conservation? If you solve a Poisson equation for pressure, try a stronger convergence criterion and see if that helps.

Thank you for the message. I think there is no error in the QUCIKEST as the mass is conserved if the eddy viscosity is kept constant. If I calculate eddy vicosity using Smagorinsky model, the mass is not conserved. If you can help !!

The scheme that you use does not seem to conserve energy, and the dynamic model does not seem to provide enough dissipation. Read the paper, "Fully conservative higher order finite difference schemes for incompressible flow " by Y Morinishi, TS Lund, OV Vasilyev, P Moin - Journal of Computational Physics, 1998

Also, some LES users limit the amount of viscosity i.e they set a constraint: nu + nu_T > 0 where nu is the kinematic viscosity and nu_T is the LES obtained viscosity. This is in addition to maintaining nu_T > 0. See if this helps stabilize your solution.