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[Bruno Chareyre <question663459@xxxxxxxxxxxxxxxxxxxxx>]

Question #663459 on Yade changed:
https://answers.launchpad.net/yade/+question/663459

Bruno Chareyre proposed the following answer:
> "a problem that would depend both on pressure gradient and pressure
average could not be simulated using periodic boundaries, since such a
problem would not show a periodic pattern from one cell (or window) to
another."

That's absolutely correct.

> "-P -- 0 -- +P / -P -- 0 -- +P / -P -- 0 -- +P"

The pressure drop per period (i.e. the macroscopic pressure gradient gradP) can be calculated by taking any two points  separated by a distance k*L, with L the period length.
E.g. starting from the first point in your sequence and going forward by L:
> "-P -- 0 -- +P / -P"

gradP = -P - (-P) / L = 0

More generally a periodic flow problem necessarily leads to P(x)=a*x + p(x), where a is the macroscopic gradient and p(x) is a periodic fluctuation, so that grap(P)=dP/dx=a+dp/dx is a truly periodic function (and velocity as well since v=-k(grad(P)). 
 
 Cheers 
Bruno

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