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Why decreasing time step makes diffusion more significant for diffusion equation? |
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#21 | |
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Quote:
So to sum up: it appears to me now that the LTE will not increase by simply reducing the time step size; rather, the diffusion-like situation is due to the summation of errors for longer iteration. Am I correct? |
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#22 | |
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Filippo Maria Denaro
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Quote:
However, the evaluation of the time accuracy makes sense if you fix dx at a value quite low. |
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#23 |
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Ok, so anyway, to be simple enough: just make sure reducing dt and dx at the same time, right?
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#24 |
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Filippo Maria Denaro
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#26 |
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I re-ran my code with cosine wave instead of Dirac function, and with time step size decreased, the wave just diffuses faster; but eventually, the inf norms of the waves are almost of the same magnitude.
So I guess it is not accurate to say "more diffusion"; it should have be "diffuses slightly faster". |
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#27 |
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MOHAMMAD UMAIR
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The initial condition should not have a sudden jump or discontinuities. Try to adjust time-step so that Pe becomes less than 2. Note that Pe<2 doesn't necessarily mean pure diffusion. If doesn't solve solve your problem then reduce dt even further.
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#28 |
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I am a little bit confused by your notation: does your Pe stand for cell Re # or something else?
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#29 | |
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Quote:
the velocity a = 1, diffusivity = 1, and the mesh size dx = 0.05, so I guess the cell Re is much smaller than 2, and it should have not appear to have excessive diffusion for this reason.. I guess |
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#30 | |
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Filippo Maria Denaro
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The Pe_h<=2 is for the cell number, not for the global number. However, it does not depend on the time step but only on the mesh size. |
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#31 |
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Filippo Maria Denaro
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If you consider the physics you want to resolve, the global Reynolds (o Peclet) number is so small that you have a real physical diffusion that smoothes out your initial solution very fast.
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Tags |
diffusion equation, time step size |
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