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How do I select a time step size for my transient simulation?

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AcuSolve uses a semi-implicit predictor/multi-corrector time integration algorithm that places no stability limits on the time step size. Therefore, the time step size is selected based on the physics of the problem, and not the stability constraints of the numerical method. This allows users to perform transient simulations with ease without the need to iterate on solution settings.

When performing unsteady RANS simulations, the timestep should be selected to resolve the transient phenomena of interest in the simulation. For example, in the case of vortex shedding behind a bluff body, the timestep would be set to resolve the shedding frequency. For most cases, resolving the shedding cycle with 30 time steps per period is sufficient to get a good estimate of the magnitude and frequency of the fluctuating forces on the body.

When performing LES and DES simulations, the timestep size needs to be set according to the size of the turbulent eddies that you expect to resolve. For LES and DES, the size of the turbulent structure that the model can resolve is closely tied to the local element size. Therefore, the time step size should be related to the element size. Therefore, it is suggested that the following formula be used to determine the appropriate time step size:

Δt = CFL* Î”x/umean

Where: Î”t=time step size, Î”x=characteristic element size, and umean=mean velocity, CFL = Courant-Friedrichs-Lewy number.

The CFL should be set to ~5-10 or less for DES simulations. For LES simulations where very small turbulent structures are of interest, the CFL number should be set to approximately 1 for the highest accuracy.

It should be noted that these are only guidelines to use for setting an initial time step size. A time step sensitivity should be done to determine when the solution becomes time step independent.


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