About the accuracy of DNS with spectral method and FVM method
As known, the usual way to perform a DNS is the pseudo-spectral 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? |
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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 micro-scale frequency is well resolved by ensuring that pi/h is far from it |
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A Tool in Turbulence Research): Code:
It is straightforward to show, using So it however shows the spectral method is somewhat more accurate in the same resolution. What's h mean in the formula 'pi/h'? |
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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 half-width 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? |
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- 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 de-aliasing 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 |
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So how can I make Crank-Nicholson more stable? until now, the only thing I can do is to use a smaller timestep size when the calculation crashed. |
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Generally, the codes us CN for the diffusive terms and Adams-Bashforth 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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