[Tushar_Telmasre]

I have learnt in theory that Implicit discretization does not have any convergence criteria and it will give you solution for any time step value. But why does I keep getting "AMG solver: divergence detected" error message? Even though the grid size and the time step value I give are exactly the same as the paper I am trying to replicate.

Can anybody comment?

[LuckyTran]

Probably because you learned this theory for a completely different problem, i.e. the heat equation.

Besides, a fully implicit discretization of the advection operator can converge towards the fixed point solution of no-flow. Hence, the fluxes are solved implicitly, but the advection operator is often discretized explicitly.

Also the A in AMG means algebraic. It is a solution accelerator and the AMG process is not the same as solving the linear system of equations. Divergence of the AMG is not the same as divergence of the solution of the linear system of equations so the theory is not really applicable. Although for all practical purposes the solution has diverged. Can it diverge and why it has diverged means something different.