hi all could anyone tell me how to calculate the time step required for convergence in a transient analysis. now in my work I calculate the time step by assuming an appropriate courant number and by knowing the grid size and the velocity I calculate the time step. I would like to know wether this is correct or it should be done in a different way. thanks in advance.

For a single equation, The maximum time step for convergence depends of time discretization (implicit vs explicit) of the different terms (source, convection, diffusion...).

For a system of equations, it is far more complicated since these systems are usually non-linear. Even though they are linearized, the maximum time step to insure convergence can be still different (larger or smaller). But, the maximum time step calculated for the single equations of the system can be a good approximation.

For exemple, I use an implicit discretization scheme to solve a natural convection permanent flow problem. Even though my scheme is supposed to converge for what ever time step I use for a single equation, it won't converge if my time step is too large (since I have a system on non-linear equations to solve). Usually, What I do for these systems is start with a dimensionless time step of 1. If it doesn't converge, I use 0.1 and so one...

Often, when you get more experienced (Have solved a similar problems), you can quickly guess an adequat time step.

Personaly, I try to avoid explicit schemes. I don't want to wayste my time calculting "the best time step" and see my system diverge too often. Specialy, when you have to solve incompressible flows, if you use too many time steps, you will waste an awfull lot of time solving the poisson type equations involved with the projection. But, this is a personal opinion...

thanks a lot