Realizable k-epsilon model k-residual
I am modeling an atmospheric boundary layer (on a 2000 m by 300 m grid where the cells are all 1 m by 1 m, uniform), over flat terrain (roughness lenght = 2 cm), and with a forest of height H=25 m starts at 5H from the inflow boundary, and is 10H long. The forest is not a part of the mesh in any way; instead it is represented by source and sink terms (in the form of user-defined functions) added to the momentum, TKE, TDR equations.
I'm using the Realizable k-epsilon closure model with the pressure-based solver, and the "coupled" pressure-velocity scheme with a Courant number of 200 and explicit relaxation factors both set to 0.7. My spatial discretization settings are: Gradient: Least-squares, Pressure: PRESTO!, and Momentum, TKE, and TDR: 2nd order upwind.
I'm getting a really strange result in my residuals that I'm hoping someone has seen before and knows how to remedy. The residuals fluctuate slowly in the first few hundred iterations, but show a strong downward trend after that (other than the k-residual). After 14500 iterations, the continuity residual is just less than 10E-6 and the x-velocity, y-velocity, and epsilon residuals are all less than 10E-10. However, even though the k-residual got down to less than 10^-3 in the first couple hundred iterations, at around 200 iterations it goes up and stays at exactly "4.0000E-01". This value (0.4) is exactly equal to the value I set for the under-relaxation factor for k. If I change the under-relaxation factor to 1.0, the residual changes to 1.0 in one iteration, and stays there. Similarly, if I change the under-relaxation factor to 0.001, the under-relaxation factor changes to 0.001 in one iteration and stays there. This only happens when using the realizable k-epsilon closure model. I've tried using the standard and RNG k-epsilon models, but so far I haven't been able to get convergence with those (I wouldn't expect the those to do as well anyway).
I've looked at countour plots of k (and many other parameters) at various points in my simulation after 14000 iterations, and I can't see any change in the countour plot of k (or any other parameters). The plots all look like I'd expect them to.
I know I could change the under-relaxation factor to be equal to the tolerance I set for the residuals and attain what FLUENT would call "convergence" that way, but I think that would be an artificial convergence. I need to know that my solution has truly converged. (I really need to be able to defend my results!)
Has anyone ever seen similar behavior from the k-residual (or any other residual) before? If so, is there a fix? Also, is there any way to tell if my solution (for k in particular) is essentially converged, even though the residual is only as low as the associated under-relaxation factor?? Any help or advice is appreciated! Thanks!
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