The effects of BCs and the initial conditions on the final results
 

Dear Friends
Does anyone know any paper which investigated the boundary conditions or initial condition effects on final results of two phase flow simulation?
I have simulated ship motion and its wave propagation by Fluent software with different BCs (velocity inlet or pressure inlet) and initial conditions (zero velocity or equal inlet velocity). The results of the simulations are completely different. In addition I did simulate by MRF approach and stationary, again the results are different.
Thanks for your help in advance

based on theoretical knowledge of your focused problem, you can select suitable BC. I never saw any papers on this kind of research. So, maybe to take time to study theoretical knowledge is what you should do. My advice.

...but theoretically I see correct that different BC and initial conditions drive to different solutions

Assuming the uniqueness of the steady-state solution for 3d N-S (which there is no proof for that fact to be true...) the initial condition should not have an influence on the steady-solution. That being said, the transient domain will obviously be altered by a different initial condition.

In my opinion, there is no reason to think different boundary conditions will lead to the same solution, unless you specify an equivalent boundary. As exemple : after running a velocity inlet solution, you could export the pressure field on the inlet, and specify a pressure inlet with that pressure field, which should therefore lead to the same solution.

Velocity inlet BC and pressure inlet BC are different in fluent, it preserves velocity and total pressure respectively. So difference in results are expected.
Initial condition will not lead to different solution. But the path of convergence will get affected. Probably one of the conditions is not properly converged. (For convergence, don't just go by residual, some times residual settle faster than the flow quantities)

Could you please refer to some related literature, textbook or any resource either theoritical or practical which describes that the Initial Conditions do not affect the final results but only the convergence path ?


Thank you in advance!

This, I think, is a too much diffused misconception. There isn't, as a matter of fact, an ensurance that, for whatever initial condition, the same problem set up will give the same final answer for a steady problem. This is even more so if we don't consider the solver that is used.

There are, indeed, cases where multiple solutions are compatible with the given problem setup, a very well known one being the 2D laminar sudden symmetric expansion. But also for turbulent flows with RANS models, the fact itself that not all the initial conditions will help convergence is again signaling the same issue.

In practice, when dealing with nonlinear problems, it is frequent that multiple solutions exist and proper initial solutions are needed to pick up the relevant ones. This is because most resolution methods are Newton–Raphson like and will typically converge to the nearest reachable solution, if any at all, with respect to the initial condition.

Thank you for your advice and excuse me for my late reply!

So, it depends on each and every case. Just to refer to my case which is a turbomachinery CHT simulation, I cannot get a convergence for the CHT without assign the appropriate boundary conditions for a previous non-CHT. The solution of the non-CHT is somewhat close so that is a fact that supports your statement.