# Dual-time stepping CFL number

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 November 25, 2009, 09:42 Dual-time stepping CFL number #1 Senior Member   Join Date: Apr 2009 Posts: 118 Rep Power: 10 Hi there I'm trying to use Jameson's Dual-time stepping technique in an implicit simulation. I have a question regarding the time-step size. I know that I can use large CFL numbers for the pseudo-time step. But what about the physical time-step? I've been told that I have to use a CFL number of 1 for the physical time-step for time accuracy and indeed this is what I observed from my simulations. Can anyone give me any reasons why this is so? Thanks.

 December 1, 2009, 09:58 #3 Senior Member   Join Date: Apr 2009 Posts: 118 Rep Power: 10 Thanks very much for the reply. That makes a lot of sense. I was confused earlier as I thought people referred to Jameson's Dual time-stepping method as an implicit scheme. I just have the following questions 1) I want my calculations to be done unsteadily and it has to be time-accurate as I want to capture the transients. So I understand that this sets a physical time constraint. I was told that this physical time constraint comes from the CFL where the flow should move one grid-cell within the time-step. This is how I have been fixing the physical time step. I don't really know what other physical time steps I could use as I don't know much about the turbulent time scales of the problem. 2) So in Jameson's scheme the inner iteration is solved explicitly like normal steady RANS? Thanks again

 December 2, 2009, 00:45 #4 New Member   Vinayender Join Date: Jul 2009 Location: India Posts: 24 Rep Power: 10 Certainly dual time stepping is not implicit time stepping, but it uses implicit time stepping in pusedo time step and explicit time stepping in real time marching, comming to your questions, 1) for example, say you are solving for a problem in which physicals time scales are order of 0.1 sec, means what ever significant flow changes happens that will happen only in time scales of order 0.1 sec. In such senario your time scale in the solver is sufficient to be of same order to capture that significant physics. If you are solving the same problem using the explicit scheme, then the time scale will be decided on numerical constriant that is using CFL(depends on the robostness of each scheme) and the grid size. and if this time step computed using this of the order of 0.01 sec. Using this time scale you will end up with increase in no of iterarations to atain the solution at a given time step. To sumarise, your physical time steps of 0.1 sec is good enough to attain the solution at a given time level, but your numerics (scheme and grid) will restrict you to use that time step and ending up taking smaller time steps and needs to solve for more iterations (roughly 10 times more for this example) 2) outer or main loop uses expicit to march in real time and inner main loop uses implicit time step to march in pesudo time step __________________ Thanks , Vinayender

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