under relaxation & Periodic Flows
 

-What is the difference between under-relaxation and false time step? What are the advantages and disadvantages of each one?

-For problems which have a steady state

we stop calculations when time derivative is zero. What about periodic flows for example flow past a circular cylinder?

under relaxaation scheme is a power scheme during Iteration.I have used it in FDM ,but widely used in FVM.good for retarded convergence.yet stable.When periodically motions are there no decay solutions with respect to time will observed.dont know about false time step..know about false diffusion!

Dear friends:
For steady problem, when we use the unde-realxation, you can find that the discretized equation is equivalent to the unsteary problem.

Dear Ardalan,

Under relaxation is generally employed when the code shows a tendency to diverge and is therefore more a stabilization tool. False time or pseudo time stepping actually is a convergence acceleration procedure, where ideas from steady--state solvers can be employed for a genuinely unsteady problem. It is possible that solvers might use both these concepts. For periodic problems, as the name suggests we stop the code when a periodic state is acheieved, in other words, the mean of integrated coefficients like Cl and Cd are invariant with time.

Regards,

Ganesh

above masters,where could i find some books about these tow concepts?i really want know them,thanks!