Switching from linear to second order methods
 

Hello
I have been simulating an aircraft using the SA turbulence model. Mesh quality is good. Steady state.

I have been having divergence problems when I run it with these settings: Coupled with time factor 0.1, green gauss node based, second order discretization.

So, I decided to run a first order analysis and then use that to initialize my second order case. The first order uses SIMPLE and first order for all discretization parameters. I decreased certain under relaxation parameters. This offers stability and even converges.

When do I switch from the first order to the second order? Is there a recommended value that the residuals need to drop below for me to make the switch or should i switch after it converges?

It depends on the problem at hand.
 

It depends on the stability, mesh quality, and general problem setup. If your residuals have fallen to below 1e-4 then it may be safe to switch to a higher order scheme. First what other solution variables are you monitoring for convergence? Are you checking the velocity magnitude, pressure changes, turbulence quantities etc. ? In general when judging for solution convergence you must ALWAYS monitor important variables and only when they have stopped changing or they have reached a periodic steady state then do we consider it converged. If you are seeing significant fluctuations in solution variables this is indicative that your problem has significant transients and a steady state solver is not appropriate. Residuals only tell us so much it is just as important to monitor flow variables. In terms of mesh quality, you mentioned you are studying aircraft aerodynamics, is your mesh quality truly sufficient? Normally to get meaningful results you must have around 15-30 nodes within the viscous sublayer of the boundary layer. What is your y+ ? Having a satisfactory y+ can be very challenging and often requires large CPU time and RAM. Better to simplify the analysis to a single wing etc.

My y+<1 for all regions of my aircraft.
I am monitoring the axial and normal forces of the aircraft and also of every body of the aircraft (wings, ht,vt,fuselage,booms).
I calculate the lift and drag coefficients from these values for the different angles of attack I need.

For the moment, I have let my low order method run till all residuals drop below 1e-6. I then switch to the higher order. Conitnuity and nut start from 1e-2 and 1e-4 for this, but my momentum residuals start from 1e-7.

I would like to know if this approach and results are what is accepted/followed ?

That is a good approach. Once you switch to second order schemes then you should wait until all your important flow variables stop changing. In particular I would monitor my lift and drag coefficients and once they stop changing in addition to the residuals falling below an acceptable criteria would I consider the flow converged. You should also consider using Mesh adaption to verify that the solution is truly mesh independent. So refine the mesh using high pressure gradient criteria etc. Especially if you are dealing with high angle of attack with flow separation. It is well known that SA and most RANS models do not handle flow separation very well, although k-w SST is possibly the best. Also you mention that your y+ is <1 and thats good but like I said most high speed aerodynamic flows require anywhere from 10-30 nodes in the viscous sublayer not just a single cell.

By the way there is a checkbox for higher order term relaxation which is like adding an under-relaxation to the 2nd order part. It will act like 1st order when the solution doesn't want to behave and 2nd order when the solution is behaving. In short, it's automatic switching between 1st and 2nd order if you just click the check box.

Thanks for both the replies.
I'll look into the higher order relaxation and might give it a go as well.