# Why decreasing time step makes diffusion more significant for diffusion equation?

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February 16, 2018, 12:34
#21
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Quote:
 Originally Posted by FMDenaro I checked in my old notes and I extracted the LTE expression, it appears clearly that, provided that the dx allows to get the Reynolds cell number <=2, you have a global positive diffusion coefficient. Now the issue is that if you compare the solution at some time T, when you decreases the time step you need more iteration to reach that time and the error effects summ.
Thx very much for your file !

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?

February 16, 2018, 12:49
#22
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Filippo Maria Denaro
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Quote:
 Originally Posted by TurbJet Thx very much for your file ! 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?
Well, that depends also on the value of the Re cell number you used, if it is greater than 2 then it introduces an anti-diffusion effect.
However, the evaluation of the time accuracy makes sense if you fix dx at a value quite low.

February 16, 2018, 12:54
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Quote:
 Originally Posted by FMDenaro Well, that depends also on the value of the Re cell number you used, if it is greater than 2 then it introduces an anti-diffusion effect. However, the evaluation of the time accuracy makes sense if you fix dx at a value quite low.
Ok, so anyway, to be simple enough: just make sure reducing dt and dx at the same time, right?

February 16, 2018, 13:09
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Quote:
 Originally Posted by TurbJet Ok, so anyway, to be simple enough: just make sure reducing dt and dx at the same time, right?
yes, right

February 16, 2018, 13:09
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Quote:
 Originally Posted by FMDenaro yes, right
appreciate it.

February 17, 2018, 18:20
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Quote:
 Originally Posted by FMDenaro yes, right
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".

 February 18, 2018, 01:14 #27 New Member   MOHAMMAD UMAIR Join Date: Feb 2017 Location: ALIGARH, INDIA Posts: 3 Rep Power: 9 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.

February 18, 2018, 03:01
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Quote:
 Originally Posted by mohd_umair 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.
I am a little bit confused by your notation: does your Pe stand for cell Re # or something else?

February 18, 2018, 03:05
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Quote:
 Originally Posted by mohd_umair 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.
If you mean by cell Re #, in my case (simple enough),

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

February 18, 2018, 03:43
#30
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Quote:
 Originally Posted by mohd_umair 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.

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.

February 18, 2018, 03:45
#31
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Quote:
 Originally Posted by TurbJet If you mean by cell Re #, in my case (simple enough), 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
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.

 Tags diffusion equation, time step size

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