Uniquesness of the solution
 

Hello,

this is a mathematical question but I would like to clarify that with respect to ocassional comutational difficulties.
Is the numerical solution of Reynolds averaged NS equations unique within prescribed tolerance? The issue we all sometimes encounter: running a steady state analysis being initialized from another case, and the solution does not develop as stable, oscillates and you cannot force it to get better, simply speaking. But by initializing from another case or no initialization leads to much different computational progress and different result in fact. So, may that be caused by the innate properties of the equations that the solution may ''fall'' locally into a state from which it cant move to the desired (''correct'') state? Can this be a property of the equations for given boundary conditions not only due to smootheness of discretization and convergence limit? Or is the solution unique and this is caused just by the numerical limits that cut the possibility for the solution to move into different state?

Some times yes, sometimes no. It is flow dependant.

Your other comments are interesting. Yes, there is a numerical accuracy component to this. Numerical inaccuracy can cause all sorts of non-physical behaviour.

But the Navier Stokes equations allows:
* Steady state, unique solutions (eg lid driven cavity at low Reynolds number - it does not matter what initial condition you specify the final flow is the same and steady)
* Steady state, non-unique solutions (eg detached flow in a diffuser - it can attach to one wall or the other in the diffuser. Which wall it attaches to depends on the initial conditions or asymmetric forcing you use. The final result will be steady state, but it could be attached to the top or bottom wall)
* Transient, non-unique (Von-Karman vortex street, flow around a bluff body etc).

Some background reading for you:
https://en.wikipedia.org/wiki/Fluidics
https://www.google.com/search?q=flui...OZagWGeK_NQDkM

Glenn's examples are great.

However, I am a bit blunter on the answer. CFD is nothing more than a root finder on a complex non-linear system of equations (PDE+Algebraic ones).

Because it is a non-linear system, it is highly possible that there are multiple roots. In some flow regimes, the non-linearities are weak and the system is fairly linear, and why the linearized equations produce very accurate solutions.

On top of the above, the numerical method used to solve the system could introduce false roots. Also, some methods can approach one of the roots easier than others, or none at all (stiff systems).

My 2cents