Does Guo’s second-order external force term really change viscosity?

[aaron]

Hi,

According to Guo’s second-order external force term introduced in LBM (DOI: 10.1103/PhysRevE.65.046308), the population is updated by a shifted term as:

f(x+dx, t+dt) – f(x,t) = -(f-feq)/tau + (1-1/(2tau)) F

here f is shifted from the original population by 0.5*(Omega + F), where is the non-equilibrium term of the original population.

Someone pointed out that since the new τ derived from the second-order scheme is effectively increased by 0.5, the viscosity is thus changed to tau cs^2 instead of (tau – 0.5) cs^2.

My question is: It makes no sense that the viscosity changes simply due to a rearrangement of the population iteration scheme, since the final equilibrium distribution is always accompanied by tau not tau+0.5, if we decompse the Omega and fully unpack the new population.

This mathematical trick should not change the physical interpretation, because if we set F to zero, it would make no sense for the viscosity to increase, even under a second-order force scheme.

Thank you for your reply!

[stephan]

Dear aaron,

thank you for your post.

I am not sure, if I understand this correctly.

From my point of view, there is no change in viscosity whatsoever due a specific forcing method.
This happens only, if you formulate the force to actually do this.
But that’s a matter of the force itself, and not of the method you use for forcing.
Please have a look in the Krüger et al. 2017 book.
There is a specific chapter that compares all the forcing schemes and explains the effects they have.

BR
Stephan

[Author]

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