I went through the codes I mentioned above:
The following solvers were good but were licensed under GPL
DUNS 2d/3d navier Stokes - GNU GPL license 2.0
Channelflow - GNU GPL2
OpenFlower - GPLv2
PETSc-FEM - GPLv2
Tochnog - GPL

One under BSD but it asn't that good - Clawpack
dolfyn - Apache
Featflow2 - Not listed

These had NS tuorials:
HiFlow - LGPL v3 http://www.numhpc.org/HiFlow3_Typo/fileadmin/tutorials/tut_Navier_Stokes_2012_03.pdf
Nectar++ - Spectral/HP Emement method - http://www.nektar.info - MIT License
http://www.nektar.info/wiki/3.3/UserGuide/Tutorial/IncNavierStokesSolver
CFD2D - MIT

The ones with MIT license are really good. Especially Nector++ which uses Spectral/HP method.

News pertaining to algorithms:
- SIMPLE cannot be used under FE context.
- I went through GEORGE EM KARNIADAKIS & SPENCER J. SHERWIN Spectral/hp Element Methods for CFD.
It required strong mathematical background to understand which I do not possess.
- Chorin-Temam projection method- Currently going through it.
- PyAMG - Jacobian-Free Newton-Krylov code to solve the Navier Stokes equations : Christine sent me no response in spite of a reminder.
- Matrix preconditioning techniques for GMRES - I do not know about matrix preconditioning. I downloaded some papers in order to understand it.
If you know about any good resource on preconditioning then kindly give me the link.

There are two potential sources of numerical instability in the Galerkin finite element solution of steady Navier-Stokes problems. The first is due to the treatment of the convective term and manifests itself in high Reynolds number flows when unresolved internal or boundary layers are present in the solution. The second source of potential instability, is an inappropriate combination of interpolation functions for velocity and pressure.
Stabilized finite element formulation is used. We have an example of it. Is it not robust R.?

PS. Professors in my department do not use FEM for fluid, but today I came to know about a professor of Aerospace who uses FEM for CFD. I have mailed him for an appointment.

On Monday, 8 July 2013 19:15:53 UTC+5:30, Ankit Mahato wrote:

Some more info:
Applying a Newton or Picard iteration produces a system of linear equations which is nonsymmetric in the presence of advection and indefinite in the presence of incompressibility. Such systems, particularly in 3D, are frequently too large for direct solvers, so iterative methods are used, either stationary methods such as successive overrelaxation or Krylov subspace methods. Krylov methods such as GMRES, typically used with preconditioning, operate by minimizing the residual over successive subspaces generated by the preconditioned operator.
Multigrid has the advantage of asymptotically optimal performance on many problems. Traditional solvers and preconditioners are effective at reducing high-frequency components of the residual, but low-frequency components typically require many iterations to reduce. By operating on multiple scales, multigrid reduces all components of the residual by similar factors, leading to a mesh-independent number of iterations.
For indefinite systems, preconditioners such as incomplete LU factorization, additive Schwarz, and multigrid perform poorly or fail entirely, so the problem structure must be used for effective preconditioning.[1] Methods commonly used in CFD are the SIMPLE and Uzawa algorithms which exhibit mesh-dependent convergence rates, but recent advances based on block LU factorization combined with multigrid for the resulting definite systems have led to preconditioners that deliver mesh-independent convergence rates.[2]

[1] http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=298722
[2] http://www.sciencedirect.com/science/article/pii/S0021999107004330

On Friday, 5 July 2013 17:23:57 UTC+5:30, Robert Cimrman wrote:
On Fri, 5 Jul 2013, Ankit Mahato wrote:

>
>
> On Friday, 5 July 2013 15:39:07 UTC+5:30, Robert Cimrman wrote:
> On Thu, 4 Jul 2013, Ankit Mahato wrote:
>
> > Hi R,
> >
> > I did some more digging from the implementation point of
> view and came
> > across some interesting things:
> >
> > This tutorial demonstrates the solution of Incompressible
> Navier-Stokes
> > Equations using Fenics. it uses Chlorin's method[1] to
> solve the problem.
> > This project was very awesome.ï¿½
> >http://fenicsproject.org/documentation/dolfin/1.2.0/python/demo/pde/navier-stoke
>
> > s/python/documentation.html
>
> That looks feasible as well, although it is for
> time-dependent problems. A
> stationary solution (if existing) could be obtained by
> stepping in time
> til nothing changes.
>
> (Sidenote: fenics is a cool project with many interesting
> ideas - good
> place for insiration.)
>
>
> Are you suggesting to use the dolfin module or to use Chlorin's method?ï¿½

The method. Dolfin itself is bigger than sfepy :)
ï¿½
> > Other Implementations:
> > ï¿½* ï¿½Parallel Spectral Numerical Methods/The Two- and
> Three-Dimensional
> > ï¿½ ï¿½ Navier-Stokes Equations-http://en.wikibooks.org/wiki/Parallel_Spectral_Numerical_Methods/The_Two-_and_T
> h
> > ï¿½ ï¿½ ree-Dimensional_Navier-Stokes_Equations
> > ï¿½* ï¿½2D Navier-Stokes solver implemented as a Python package
> with Python
> > ï¿½ ï¿½ modules and C++ extension modules. It uses the finite
> difference
> > ï¿½ ï¿½ method on a uniform, rectangular grid. It handles
> single- and
> > ï¿½ ï¿½ two-phase incompressible, Newtonian, laminar flow with
> obstacles.
> > ï¿½ ï¿½ -https://code.google.com/p/kmkns/
>
> There is a thesis to download - might be interesting.
>
>
> Yes, but it is using Difference method.

Ok, then it is not directly applicable.

In general, SfePy can assemble the matrices A,
B forming a saddle point system with block structure [[A, B], [B^T, 0]] -
methods for solving that, making use of A, B, might be usable no matter
the method A, B were created (FEM, FVM, FDM).

>
> I think it would be easier to follow a paper/thesis, as
> details in code
> often differ. But you can try, yes. Note that sfepy is
> BSD-licensed, so we
> cannot use snippets/functions from GPL-licensed codes.
>
>
> So we can use any code with BSD license. right?

Yes.
ï¿½
> > Someone was using PyAMG to develop Jacobian-Free
> Newton-Krylov code to
> > solve the Navier Stokes equations :
> >
> https://groups.google.com/forum/#!topic/pyamg-user/HXrXTyvXPpw
>
> This could be really interesting - maybe you could ask the
> person on how
> far that project got?
>
>
> i had already dropped a mail on her email-id. Waiting for her reply.

Good!
ï¿½
> So, it looks there are lot of things I need to look in depth now.

Yes, it is not easy to choose. For the beginning, I would rule out codes
that are not FEM-based. As for algorithms, I would look at operator
splitting and other iterative techniques.

Thanks for looking into this, it will be very useful.

r.