# Newtons methods for unsteady problem

Hi everyone,

I meet a problem with implementing the unsteady NS equation with Newton method. I need to implement a periodical boundary condition on the inlet. However it seems that with Newton method, the convergence is not very well, the message shows that the SNES Function norm is always at a high value like XXe-1 to XXe+1 and it doesn’t go further down. Do you have any suggestions to improve the situation? Thank you!

I here enclose my code for checking, thank you!
NewtonNS.edp (5.2 KB)

Best wishes
Dongwei

I cannot run your script because it needs an input file that you didn’t share. You mention that you have periodic boundary conditions, but I don’t see any periodic `fespace` in your file.

Sorry I forgot to attach the inlet, here it is:
LCA_inlet_FreeFem_new.zip (10.4 KB)
mesh.zip (80.5 KB)

This is a txt file where I read in the inlet max velocity (it’s a parabolic profile). The way that I implemented the periodical BC is using this data repeatedly by `+ on(4, ux = uaugm[(tstep-1)%1000]*(y-1)^2-uaugm[(tstep-1)%1000], uy = 0);`

Also due to the implementation of Newtons method, I calculate the augmentation of the velocity of each timestep from the velocity list `ulist` which is the argument `uaugm` here.

But I am not sure it is the correct implementation for the situation

Still does not run as there is no mesh. But that’s not the proper way to impose periodic boundary conditions anyway.

Ok, I see. Could you point me to an example of implementing periodic BC in the context of Newton methods?

Sorry I just realise that my question may not be precise. I may have used a wrong term. The periodic BC I mean is having a repeating pattern inlet velocity using the data like a pulsatile flow instead of having the outlet as another inlet.

Even the first nonlinear system cannot be solved. How did you implement your two varf? Does it work with a Newton linearization implemented “by hand”? My best advice would be to start from something that works, e.g., a steady-state Navier–Stokes script, and then add time discretization and then your forcing term. It’s difficult otherwise to debug these multiline varf.

I highly doubt your `vRes` varf is correct. Your Dirichlet boundary condition on label 4 does not depend on the previous residual, which can never go to 0, hence the stagnation. At convergence of `SNESSolve`, keep in mind that `vRes(0, v)` should evaluate to a vector whose norm is close to 0. Here, that’s impossible since you have `on(4, ux = uaugm[(tstep-1)%1000]*(y-1)^2-uaugm[(tstep-1)%1000], uy = 0)`. Maybe it should be `on(4, ux = ucx-uaugm[(tstep-1)%1000]*(y-1)^2-uaugm[(tstep-1)%1000], uy = 0)`?

Dear sir,

i have a quetion, what’s the default precision of a real number in FreeFem? Can i change the precision of it? May the default precision setting influence the results?

For example, in MATLAB, format long means 16 significant digits.