3D Finite Element for incompressible flow
 

Hello,
I am writing a finite element code for solving incompressible navier-stokes equation. to solve the system of linear equations I am using Bi-conjugate gradient algorithm as it works with unsymetric system. I am not getting a converged solution and the residuals becomes 'nan' in 2nd or 3rd iteration. Although I can not post my code here, I would like to know few things if possible.

1. Does the global stiffness matrix have to be diagonally dominant ? In my case it is not. so in that case I am making a mistake in basic formulation.

2. If diagonally dominant is not a requirement for N-S equations, what preconditioner is best suited for unsymmetric system ? I am using ILUpreconditioner. Just wondering if the problem is in using preconditioner.

3. I do not have any zeros on the diagonal. What are the general scenarios when FEM solution diverges or becomes 'nan' ? (Its hard to answer without the code but I would appreciate answers if anyone has faced this problem before)

Firstly I thought that problem could be in mixing the pressure and velocity unequal interpolation function. SO I removed all the pressure terms and continuity equation. It remain like a 3D heat equation. Still the problem persists. I doubt that its the preconditioner which is causing it.