Can all solution methods converge?
 

Hello Everyone,
I'm relatively new in CFD so excuse any mistakes, or lack of general knowledge that might appear from this question.

Background:
I'm running a case study on a NACA4412 airfoil (2D with boundaries being 20m from the airfoil in all directions at the least, while the airfoil length is 1m).
The inlet is a velocity inlet of 44m/s to achieve a Reynolds number of 3,000,000.

Purpose:
The purpose of this case study is to check all possible solution methods, and compare their accuracies with published NASA experimental results, compare the convergence time, and deviations. The end result will be a large graph of experimental results of cl vs alpha of all the solution methods for y+1 (from 1 to 5) and see the deviation of each method from the experimental results, including iteration time, and choosing the most optimal. Another case will be the same except this will be for y+ >30 (in my case I'm picking 50-60 as my acceptable range for my mesh). The purpose of this is again to compare the optimal methods, as having a larger y+ would allow me a less refined mesh, and thus much faster computaiton.

Question:
I have gotten convergence from a few solution methods (easiest to converge is SST k-omega). So, will every single solution method converge, and the trick is to manipulate the wall treatments, controls, and methods to reach that? (i.e coupled vs simple, steady vs PTS, first order vs second order, a mix of everything before, hybrid vs standard vs fmg-initialization) etc...
Or will some methods never converge for my case regardless of what variant (standard vs realizable vs rng k-e for example) I choose?

In others words (and I apologize if this has gotten confusing):
Will k-e always converge, and it's just a question of Realizable vs Standard vs RNG?
Will Spalart-Allmaras always converge for this case?
Will k-w always converge and it's just a question of SST vs Standard?

For more clarification, I'm tracking mass flow rate, residuals, cl, cd, cm_c4 for convergence conditions (although cd values aren't focused on as they are 2d). My convergence conditions are residuals no less than x10^-3 with no "jumps", and no significant changes in the aerodynamic coefficients, and a mass flow rate of 0.

Thank you, and apologies for any confusions.

If the airfoil is at low angle of attack, the flow is quite simple and everything I can think about should converge, especially with a good mesh. Some turbulence models like reynolds stress models might require some skill

I'm running cases from -10 to 13 alpha with increments of 1 degree.
The current benchmarking case I'm making is 10 degrees where there will be some separation, but not stalling.

Information about the airfoil (Stalling is at ~13 angle of attack, and -14 angle of attack).

Cases at aoa=0 all converged, but that doesn't tell me anything since the model is very very simple.

start with cases where you expect no stall. 0 AOA is fine, because the airfoil is cambered.

If stall is present, you can have unsteady flow and the steady solver might not converge. Different turbulence models predict different stall angles, so you may have some angles of attack where one turbulence model finds a steady solution, while the other does not.

That's what I want to find, which solver can NOT solve a stall case, or rather, which solver can solve the closest to stall. I'm trying to go in blind to confirm on my own, the quality, and differentiations of all solver/method/control combinations to find the most optimal one for my case.

According to experiment, 13.78 aoa is stall, I want to find the solver closest to that, because if a solver diverges at 9 aoa, that's only good to give me a rough Clalpha value, but not Clmax.

My question is, how do I know the solver not solving at 9 aoa (as an example) is the limitation of this solver, or my own failure to fine-tune the solver properly.

It will not diverge, it may simply not converge and start oscillating. This is just physics, stall is an unsteady phenomenon and a steady solver should not be able to see it. There are cheaty techniques that sometimes work depending on the numerical damping, but you can’t escape that much. Again, it’s just physics, no magic

For RANS models, I expect k-omega SST or reynolds stress models to be most predictive. The question is if you need a steady solver or an unsteady one. This you need to check on your own.

If you really want the best accuracy, there’s no need to go blind, a pure LES will do the job