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Compressibility in Multiphase Lattice Boltzmann Simulation

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Old   April 26, 2017, 04:31
Default Compressibility in Multiphase Lattice Boltzmann Simulation
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Hello,

I'm trying to simulate an oil-water mixture in a stirred tank using the Shan-Chen Lattice Boltzmann Method. I managed to implement it and get it running but the main issue is that the fluid is way to compressible. Now this may be irrelevant in some cases but in the stirred tank, the density of water on the top is then about 700 kg/m3 and 1300 kg/m3 at the bottom which is completely unphysical. Is this a systematic error in the Shan Chen Method and are there ways to overcome this or do I have to use an other method?


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Old   April 26, 2017, 04:53
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Try with smaller time steps and see if the problem persists.
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Old   April 26, 2017, 05:53
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Hi, yes the problem persists for small time steps and also after a lot of time steps. When initializing small oil drops with surrounding water, you can see the coalescence really nice, but there is some kind of shock wave going through the domain which I've also seen in youtube videos of shan chen simulations.
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Old   April 26, 2017, 09:20
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then you must be doing something wrong and it is very hard to tell from here.

Are you sure of your equilibrium function calculations?
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Old   April 27, 2017, 09:02
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The code seems to be implemented correctly. However the same behaviour is seen in this video "Immiscible Guy" on Youtube (https://www.youtube.com/watch?v=BQyC_j23IuM&t=37s)
There are grey and white areas that show the same fluctuations than in my simulations.

Is there a systematic error in Shan Chen Model and are there ways to overcome this? Somehow this issue is not adressed in publications.


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Old   April 27, 2017, 09:49
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I never implemented Shan Chen model so i am trying to say based on standard LBM that i have implemented in past.

Here are few things to note:

Density is just sum of probablity density functions and these functions are what you solve for. From this a direct inference is that any error in density is direct result of error in probablity density function.

The way LBM equations are derived you can recover the navier stokes equation that you see other solvers solve. This means that given no descretization errors and no temporal marching errors your solution shall follow Navier Stokes and thus mass shall be conserved.

From these two what we can infer is that any error that you see is result of (a) time marching error or (b) spatial descretization error.

Usually LBM uses explicit Euler method so if code is properly implemented and given sufficiently fine grids time stepping is major source of error. And indeed a lot of literature is devoted to this area of LBM.

For this we look at results with smaller time steps and you cofirm that it does not change situation.

So last source of error seems to be spatial descretization. Based on your comment on that youtube video , it seems like error might be in how you deal with boundary. You are either losing some mass there or gaining some mass. (This could happen in LBM) So this is next area where I would focus and check whats going on. Note that error would convect from boundaries to interior (so observe how error evolve with time).
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Old   April 27, 2017, 10:28
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Thanks for your help. I now played around and set the conversion factor for time A LOT lower than before, by reducing the gravity in lattice units. Now the difference in density still decreases linearly to the top, but the difference is now just 1015 at bottom to 985 at the top, which would be acceptable for me.

I will do some research on how to set the conversion-factors/gravity correctly and verify this with droplet rising velocity and post it here, for now this seems to do the trick.

Thanks!
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