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Time Step Unsteady Sonic/Supersonic Flow

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Old   July 22, 2008, 11:57
Default Time Step Unsteady Sonic/Supersonic Flow
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Hi For unsteady calculations what is the best way to set time step? In first thoughts here is what I did, t = min(grid_size)/speed of sound

Any comments!

Thanks a lot

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Old   July 22, 2008, 13:09
Default Re: Time Step Unsteady Sonic/Supersonic Flow
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You've essentially set the maximum CFL number to be of O(1). This may be a good starting point, or not. If your solver uses an explicit time integration scheme then this may be the best you can do. If you have an implicit solver then you may be using a lot more computer time than is necessary. Generally speaking, if you have an unsteady flow field then ask the question - what makes it unsteady? What is the relevant characteristic time, if any? For example, flow over cavities tends to resonate at certain frequencies that depend on Mach number. These characteristic times can be used to establish an unpper limit on your time step. For example, to resolve the important temporal behavior you may want to ensure that your time step remains below (characteristic time)/100.

If you are unsure of a characteristic time, running a simplified case at a variety of time steps may be necessary to establish some bounds on an appropriate value. But in all cases the physics needs to drive your selection of the proper time step (assuming your flow solver is robust enough to allow that choice). If your flow solver is not robust enough then you have to settle for what you can get.
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Old   July 23, 2008, 08:59
Default Re: Time Step Unsteady Sonic/Supersonic Flow
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Thanks ag. That was really good explanation. The flow I am trying to simulate is a supersonic/sonic jet impinging on a flat plate. And I am interested in the unsteady pressure signature on the plate. The pressure fluctautions on the plate depend on various parameters such as the nozzle pressure ratio, the distance between the plate and the nozzle exit, the plate inclination just to name a few important ones.

For this problem how can I find a characteristic time scale? I can of the rates at which shocks(when present)hit the plate. But I don't know how to find this? The flow solver I am using is WIND-US.

I would really appreciate any input on this.

Thanks again.
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Old   July 23, 2008, 09:38
Default Re: Time Step Unsteady Sonic/Supersonic Flow
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The safest (and most tedious) approach is to essentially perform a timestep study. Run a series of time steps that span a sufficient range to see if any significant behavioral changes arise. Of course, the definition of sufficient is somewhat nebulous, and can require a certain level of experience. Dimensional analysis can also provide some input on what type of characteristic time scale may be relevant. Just as a first cut, one possible time scale of relevance could be the ratio of the distance between the nozzle and plate to the freestream sound speed (acoustic feedback to the nozzle exit).
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