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I don't understand your procedure...the eddy viscosity at time n+1 is unknown and the system would be not linear... |
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the terms in the RHS require (dt/2)* for the CN integration.
However, the restriction for the time step is very important, you need a small value |
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In my case, the second term reduces the dt from 2e-3 to 1e-6 I wonder either there is a way to reduce the restriction for the second term. . I saw several papers use AB2-CN method with relatively large dt, but they didn't mention about the details. Thank you |
the LINEAR stability analysi of the CN discretization leads to two eigenvalues from which one has stability unconditionally for one but not for the other. That means the coupling with the all terms of the equations leads to a stability region (cfl,Reh) with a strong restriction in the dt at low Reh.
Considering that you have a non linear case, the constraint on the dt is clearly strong. Actually, I am used to work by letting the CN scheme for the molecular viscous term and using explicit second order AB for the eddy viscosity term. |
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But using AB for eddy viscosity term, does it reduce the CFL restriction? Do you use also AB for the viscosity of the first term, or only for the second term? |
First, the eddy viscosity can become locally high and the time scale needs to be small. Then, using an explicit AB scheme for the SGS term you avoid to work with a non-linear system having coefficents in the SGS terms.
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just using the explicit AB discretization requires eddy viscosity only at tn and tn-1, no coefficents are therefore present in the algebric system
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the stability constraint is due to the combination of the type of time integration along with convective, diffusive and SGS terms. Generallly, the CFL must be quite smaller than 1 |
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Do you know any reference which explains the discretizations in details for LES? |
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