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Question: Are Local Timestep Methods Bad?

	Posted Thu July 12, 2001 @09:00AM
	I've often wondered about the validity of attaining a steady-state solution with local time-stepping methods (aka CFL number). The problem to me seems that slowing the problem down in one area opposed to another would not yield a global steady-state solution - unless the simulation was run for a very long time even after the residuals have "converged". The residuals are small because the solution is balanced, but the transient processes are not necessarily in balance! I know these methods are necessary and very useful for cases which have a large (several orders of magnitude) timescale variation, such as jets expanding into quiescent flow, but are the solutions really correct?

	If you have really attained a steady-state solution with this method then you should be able to switch to a true global time step approach and take a large time step and see no difference in the solution (time derivatives are zero for steady state process). Problem is, I have seen solutions diverge and blow-up when performing this test of the "steady-state" solution. My question to you is, how much do you trust solutions attained wtih local time-stepping methods. Do you worry about this phenomenon? Perhaps someone can prove that local time-stepping methods do achieve steady-state results for cases with large variation in timescale.

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