Hi Hong,
Firstly, depending on the model, the mesh, the physics you are simulating, 5s could be very big or very small.
Secondly, there is a tight link between convergence and stability but stability is NOT convergence.
The definition of these two concepts are very wide and field-dependant, however:
In General, "Numerical Stability" means that the numerical error(generated by the descretization) of the scheme will not "explode" and hence stays always bounded. Stability can be conditional or unconditionnal, this means that we can garantee that the scheme remains stable only if there is a specific condition (such as CFL). Some other schemes can be unconditionally stable i.e. it remains stable wihtout any condition. For each scheme, the stability regions have to be defined.
The convergence is also difficult to explain in some lines. However, in the frame or your application, the nuemrical converngence of a solver (Conjugate gradient in your case, as for any other iterative solver) means that the solver reached the solution Xn(of the linear system AX=b) that satifies the accuracy that you have prescribed for it (by default 10-6 for CG).
To go back to your question, you can use a scheme which is unconditionally stable but you can (for some other raisons that I explained in my previous post) not converge. So the solution for you is to increase the "maximum number of iterations for solver" or decrease the time step or smooth the steep gradient in the boundary condition you are imposing.
I hope that this is helpful
Riadh
