Dear friends, I am trying to use LES to simulate the incompressible flow. I have used Smagorinsky model for eddy viscosity. My problem is if I use Smagorinsky model (C =0.16), the total mass start decreasing. If I put off smagorinsky model, the total mass is conserved perfectly. Also the rate of decrease of mass changes with the change in the value of C, i.e. the rate of mass decrease is very low if C=0.05, and rate is high if I take C =0.2. Where can be the probable error. Any advise would be highly appreciated, Thank a lot,

Do you add the SGS terms at the same time as the viscous stress term?

Also how do you enforce mass conservation? Do you solve a Poisson equation for pressure?

Thank you very much for your quick response. I am adding SGS terms at the same time as viscos terms. What I did is, I split the momentum equation into three parts 1. advection, 2. diffusion 3 pressure part. The poisson type pressure equation is derived from the continuity equations and pressure part of the momentum equations. I solved this derived poisson equation using SOR method. Also I split the mass transport equation into two parts advection part and diffusion part. Advection part is solved by Ultimate quickest and diffusion part is solved by central difference method for space and Adam-Basforth method for time. but the problem is the total mass starts decreasing the moment Smagorinsky model is put on. Any kind of advise will highly appreciated. Thanx again.

There must be some problem with your pressure solution (Poisson equation). Try to lower convergence criteria for your SOR solver and see if it helps. Otherwise there must be somthing incorrect with the way you compute SGS terms.

Hello! There's a problem with SGS. I use LES with filtering for incompressible flow and it works perfectly. If SGS is a must, then the problem is ether Puasson equation for pressure or diffusion part(where you add SGS), i guess. Convection (advection) is usually conservative, cos either it suffers divergence. I'll check my PhD for that, cos i compared SGS and filtering for compressible (shock waves interference)/inc. flows there. If i find anything, i'll post here later.

Hi Dr Nick! Thank you very much for your reply. I have doubt that I am making mistake in addition of diffusion part and SGS part. As I am doing calculation on staggered grid. The eddy viscosity is defined in the center of cell and velocity is defined on the walls of the cell. In order to add (diffusion part with SGS part), how did u interpolate eddy viscosity? As the diffusion part contains du/dt+(Adv)=(kinematic_viscosity+eddy_viscosity)*(du* *2/dx**2+du**2/dy**2+du**2/dz**2) Please advise. Thank you once again. Also please tell me which SGS model did u use for SGS terms.

It's too much for a Dr =). I've just held my PhD and still waiting for papers to be ready…

Yes, I used Smogarinsky subgrid model. Velocities are found on the edges and pressure and viscously in the center of a cell. Diffusion is defended, either as you've mentioned, or as vertex prediction (the formula is big so I won't put it here). The problem is that you have to add SGS after you have solved the Puasson equation for pressure with already corrected velocity with mass conservation equation (D=du/dx+dv/dy+dw/dz->0) cos otherwise it will suffer divergence or mass loss. Another problem here – is iterations on SGS velocity (1-st step for diffusion before presser correction and second – after) but I'm not sure that it's better way to solve mass problems. If you put SGS after you've corrected velocities, then I guess we should discuss this more detailed. Nothing else is coming to my mind now.

I hope you haven't made an error of sign and subtracted SGS viscosity instead of adding it. I would check this first.

Thankx for the message. I have added the SGS viscosity in diffusion (not subtracted)