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Old   March 24, 2013, 10:27
Default Time step for implicit solver
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Sijal Ahmed Memon (turboenginner@gmail.com)
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I am simulating low pressure turbine unsteady flow and I have couple of questions:

1. How to decide time step for the implicit solver?

2. Do we need to satisfy CFL < 1 for implicit solver?

3. Why implicit solver is preferred in commercial codes and as I understand for unsteady flows explicit solver would be better option.

4. Or explicit solver is only efficient in LES where turbulent scales to be resolved are the same order as the time step dictated by CFL < 0.2 condition?

5. For the same geometry and flow, time step is inversely proportional to Reynolds number?
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Old   March 24, 2013, 11:10
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A CFL number smaller than 1 is a stability constraint for some explicit solvers which does not apply to the implicit ones.

This partly answers question 3, because with the implicit solvers, the timestep size can be chosen according to the flow considered and does not have to fulfill a CFL criterium.

Since a CFL number below 1 is a good guess for the timestep in LES, the advantage of implicit solvers allowing for larger timesteps becomes irrelevant, since the timestep has to be small anyway.

According to Kolmogorovs turbulence theory, the timescale of the smallest eddies is proportional to Re^{-1/2}. Yet this is only relevant for DNS.
In a LES, there are different approaches to estimate an appropriate time step size, like CFL<1 for example.
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Old   March 24, 2013, 16:53
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the choice is driven by the numerical stability as well as accuracy requirements.... often, implicit scheme are not "pure", in the sense they are mixed in an implicit and an explicit part. For example, a classical integration used in DNS/LES is the Crank-Nicolson for the diffusion and the Adams-Basforth for the convection. This result in a conditionally stable scheme that is not stable only under the satisfation of the cfl<1 condition. It exists a stability region in the cfl-Reh plane.
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