iterative solution of non-linear NS equations

Hello everyone,

I am trying to solve incompressible NS equations iteratively using NGSolve. I am ignoring the incompressibility condition (using a splitting method). Hence, what I am trying to solve has a non-linear convection term on the l.h.s and a known pressure value on the r.h.s and I am solving for velocity, iteratively.

I have taken a look at the documentation the section regarding the non-linear equations and solving them using Newton’s method. I put the pressure term on the l.h.s of the equation and got Ax=0 type equation and followed Newton’s method as explained. But I am not converging and I do not know why…

Anyone has experience with this?


Here I write the equations in the way that I want to solve them. (\nu=viscosity)

u^{t+1}-u^{t}/deltat - \nu1/2(\laplacian u^{t+1}) + 1/2*(\grad u{t+1} * u^{t}) = - \grad p^{t}+ \nu1/2(\laplacian u^{t}) - 1/2*(\grad u{t} * u^{t})

Can you attach your code?