FIELD INVERSION: GMRES DOESN'T CONVERGE WHEN BETA BECOMES NEGATIVE

[alexspou]

Greetings

I am running many Field Inversion adjusting the multiplier of the production term in the Spalart Allmaras turbulence model. I have noticed that the GMRES does not converge when the beta field becomes negative at some points, which in some cases must happen as in order to match the fields of the objective function, turbulence must be destroyed in some points. Do you know how could I overcome this problem?

One idea, which is not actually the solution but partly does the job, is use for some steps, the last computed gradient of the beta field and try different steps trying to achieve the one which gives the best performance.

If you have any ideas/ solutions i would be really grateful!