Hi,
I'm trying to approximate the solution of a mixed Navier-Stokes variational formulation, as follows (note that $u = u^n$, the spatial discretization is "semi-implicit", therefore is still a linear problem):
$ \displaystyle
\dfrac{\rho}{\Delta t} \int_{\Omega} u~v~ d\Omega + \int_{\Omega} \mu \nabla u~ \nabla ~v ~d \Omega - \int_{\Omega} (\nabla \cdot v) p ~d \Omega $
$
\displaystyle + \rho \int_{\Omega} (u_{n-1} \cdot \nabla)~u \cdot v ~ d\Omega + \frac{\rho}{2} \int_{\Omega} (v \cdot u) \nabla \cdot u_{n-1} ~ d \Omega + \int_\Omega ( \nabla \cdot u ) v ~ d \Omega$
$
\displaystyle = \dfrac{\rho}{\Delta t} \int_{\Omega} u_{n-1}~v~ d\Omega + \int_{\Gamma_N} g~v ~ds $
where v and q are test functions (P1 and P1 + bubble, the minuim to satisfy the needed inf-sup condition), u and p are the trial functions (velocity and pressure), rho is the density and $\mu$ is the dynamic viscosity.
To solve the associated spatial discretized system I'm using a MUMPS solver, and works very well. But, considering the amount of memory used by MUMPS for large problems, I would like to change the solver to something like gmres+amg, but doing that I get
spurious solutions.
So the question is, what iterative solver and preconditioner is suitable for my problem? (I think is a general question for a mixed NS problem, but if someone think that I have to upload more info relative to the problem, I will).
For the record, I know this is not really a FeniCS question, but still can be useful for the community.
Greetings!
Felipe
