Hello,

I am trying to do a finite volume LES calculation using a commercial code for flow across a blunt body. I am using a steady inflow BC with 2% turbulence intensity and fixed pressure outflow BC. I am using Crank Nicholson for time advancement.

After about 600 time steps, I see that the code blows up. (Kinetic energy of the flow tends to infinity). I think there could be several reasons, listed below. Please try to eliminate them or add to them..

1. Could the instability be due to crank nicholson? I know that the method is unconditionally stable, but only in the weak sense. I know my CFL numbers (U*delta_t/delta_x) in many parts of the grid are way above unity. Could this be the problem? I don't want to use a first order implicit method to avoid it's diffusion, and I cannot really reduce the time step as it would make the computation impractically expensive.

2. Could waves be reflecting off my outflow BC and causing instability? How do I check for this? How do I remedy this?

3. I am using central differencing for my advective terms (to avoid the well known diffusion due to upwinding). Based on the cell Peclet number, I know that I cannot satisfy boundedness at every point on my grid, and this may well be the cause of instability. Does anyone have a similar exeprience? How do I get around it? Does anyone have any experience with second order upwind methods? How do they perform in an LES?

CFL numbers need to be ideally below 0.3 in LES. Reduce your time step significantly.

crank nicolson should be an implicit scheme, but it doesn't guarantee stability.

Is there a way you can look at the residuals in your computational domain, i.e. where are the locations which have the highest residuals? It might have to do with extremely fine/highly unstructured grid.

Are you using a pressure-based or a density-based formulation?

Tell us about the problem you're running, the Reynolds number, the time-step, the grid resolution etc.. and we may have a better shot at convergence.

I never did LES but some suggesations : Can you limit the kinetic energy till u have passed trasient stage and then may be remove this limit. amol