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May 20, 2014, 21:16 
About the accuracy of DNS with spectral method and FVM method

#1 
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Huang Xianbei
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As known, the usual way to perform a DNS is the pseudospectral method, even though the grid is larger than Kolmogorov scale, the calculation is expected to be accurate. While when FVM is used, I'm suggested to use a finer mesh if I want to perform a DNS with FVM.
So here I have a question: Is FVM DNS needs the grid to be smaller than the Kolmogorov scale? 

May 21, 2014, 03:29 

#2  
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Filippo Maria Denaro
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Quote:
2) Using FVM implies that the resolved frequency before Nyquist are smoothed. If your grid is correctly refined, this smoothing lies over the range of physical dissipative frequencies and the simulation is accurate. A general suggestion can be to ensure that the Taylor microscale frequency is well resolved by ensuring that pi/h is far from it 

May 21, 2014, 20:45 

#3  
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Huang Xianbei
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Quote:
A Tool in Turbulence Research): Code:
It is straightforward to show, using the modified wavenumber, that the secondorder central difference requires a mesh spacing equal to 0.26 to meet this requirement, while the fourthorder central difference, sixthorder PadŽe, and Fourier spectral schemes require mesh spacings of 0.55, 0.95, and 1.5 respectively So it however shows the spectral method is somewhat more accurate in the same resolution. What's h mean in the formula 'pi/h'? 

May 21, 2014, 21:52 

#4  
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Huang Xianbei
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I'm not sure the method I estimate the Kolmogorov scale is right,so I write down my process: The channel flow I focus on, Re=2900,Re_tau=194,FVM method is used. As dissipation rate can be estimated as epsilon=u_tau^3/l, u_tau is the friction velocity, l is the halfwidth of channel. So the Kolmogorov scale is write as : yita=Re_tau^(4/3)*l The channel dimension is 4*pi*l, 2*l, 2*pi*l in three directions, l=1m. The grid is 128*128*128 Using the former formula, yita=0.0192375031 deltax=0.098125=5*yita deltaz=0.0490625=2.55*yita deltay(max)=0.041238518=2.14*yita Is this calculation reasonable to show a acceptable grid resolution? 

May 22, 2014, 03:42 

#5  
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Filippo Maria Denaro
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Quote:
 h is the mesh size  SM are theoretically more accurate than FD/FV but the problem is that in practice you use SM on the non linear term that produces aliasing. The dealiasing techniques (filtering and so on) degrades the accuracy of the resolved high frequency and you are forced to use refined grids  this paper contains some other estimations (for LES but is useful for your aims) http://scitation.aip.org/content/aip...1063/1.3676783 

May 25, 2014, 09:06 

#6  
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Huang Xianbei
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So how can I make CrankNicholson more stable? until now, the only thing I can do is to use a smaller timestep size when the calculation crashed. 

May 25, 2014, 11:25 

#7  
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Filippo Maria Denaro
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Quote:
Generally, the codes us CN for the diffusive terms and AdamsBashforth for convective terms, that will increase the stability. However, the stability region for small cell Reynolds numbers require very small time steps 

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