Hi Wolfgang
> but if you treat the nonlinearity implicitly, and time discretized model
> will remain
> nonlinear and needs to be solved with a Newton scheme or similar. The
> appropriate solver for that system then remains FGMRES.
>
Thank you for your hints on my previous question. Now I have extended
step-57 to be time-dependent. I added a u,t term which is approximated
using backward Euler, and all the remaining terms are treated implicitly.
Newton iteration is still used at every time step. The system becomes
(A + M/dt)U = F - (\delta v, (u^{k+1} - u^k)/dt)_\Omega, BU = P, which
is similar to what we have in step-57 except the LHS(0, 0) and RHS(0) are
changed.
I'm still using the same preconditioner developed in step-57. So far it
works the simple case of lid-driven cavity flow. My questions are:
1. It doesn't make much sense to keep using the preconditioner developed
for steady NSE here, are there any simple ways to adapt it for
time-dependent problems?
2. Instead of working on better preconditioners, can I simply treat the
convection term explicitly (using the value at last time step)? The reason
is that doing so would make the LHS of the equation symmetric (I think),
which should be easy to solve. This seems to be much easier.
What is the correct direction to go (for engineering applications where
convection is significant)?
Thanks
Jie
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