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August 13, 2014, 10:34 
Time step in LES

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M. Nabi
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I am writing a code for LES. This code is based on a structured curvilinear grids with strong stretching beside the walls. In order to reduce the restrictions for time step, I used AdamsBashforth for the convection term and CrankNicholson for the diffusion term. The first term in the righthand side is ok, by using CrankNicholson method. But the second term yielded a strong restriction in the CFL number. I tried both AdamsBashforth and CrankNicheolson for the second term, but both of them needed very small dt. In the case I remove from the second term, it works fine, but including makes strong restrictions in time step. And my question: How can I remove this restriction from the second term? Is there any way? Thanks 

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August 13, 2014, 11:21 

#2 
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Filippo Maria Denaro
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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... 

August 13, 2014, 11:26 

#3 
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Right, it is unknown, but I iterate all momentum equations and the eddy viscosity (using Smagorinsky) until velocity field converges. Then use pressure correction equation, and correct the velocity field.


August 13, 2014, 11:41 

#4 
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Filippo Maria Denaro
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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 

August 13, 2014, 11:52 

#5  
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In my case, the second term reduces the dt from 2e3 to 1e6 I wonder either there is a way to reduce the restriction for the second term. . I saw several papers use AB2CN method with relatively large dt, but they didn't mention about the details. Thank you 

August 13, 2014, 12:47 

#6 
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Filippo Maria Denaro
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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. 

August 13, 2014, 12:54 

#7  
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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? 

August 13, 2014, 13:38 

#8 
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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 nonlinear system having coefficents in the SGS terms.


August 13, 2014, 21:57 

#9 
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But how to avoid having coefficients in the SGS term? Even if it is explicit, still the eddy viscosity can be locally high from time step n, and it is included in SGS!!! Do you mean we have to linearize it by, for instance, Newton linearization?


August 14, 2014, 03:19 

#10 
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just using the explicit AB discretization requires eddy viscosity only at tn and tn1, no coefficents are therefore present in the algebric system


August 14, 2014, 03:58 

#11 
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It is right, they will be known. But they will still restrict the CFL number as the value of eddy viscosity is large. Using explicit method such as AB2, lets the CFL number dependent on the size of cell quadratic, isn't it ?


August 14, 2014, 04:14 

#12  
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Filippo Maria Denaro
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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 

August 14, 2014, 20:38 

#13  
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Do you know any reference which explains the discretizations in details for LES? 

August 15, 2014, 06:03 

#14 
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Filippo Maria Denaro
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if you want, some of my papers about discretization for LES are published on IJNMF. Details are provided for projection method with AB/CN discretization


August 15, 2014, 21:57 

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August 16, 2014, 00:42 

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