Unit conversion: from LB to physical in terms of the kinematic viscosity

[aaron]

If we consider applying LBM to a 1D Terzaghi consolidation problem,
say the domain size is 0.1 m x 1 m, and the physical properties of water are:
1000 kg/m3 for density, and 1e-6 m2/s for kinematic viscosity.

Since consolidation is a quasi-static problem and the Reynolds number may be very small,
I want to maintain variable consistency by matching the kinematic viscosity in LB units as:

nu_phys = nu_lbm * (dx*dx)/dt

If the relaxation time tau is around 0.6–1.0, then nu_lbm is approximately 0.03 to 0.16,
and (dx*dx)/dt lies between 6e-6 and 3e-5.

Now, the problem is that either dx or dt must be extremely small to proceed, resulting in very high lattice resolution that makes the simulation impractical, even though the domain is not large (0.1 m x 1 m).

Do you have any suggestions on unit conversion?
Thank you for your time!

[TimBingert]

Hi Aaron,

you are exactly right! Usually in OpenLB, this job is caried out for you by the UnitConverter, i.e. you can use the UnitConverterFromResolutionAndRelaxationTime, which depending on your tau that you input, finds the appropriate timestep size based on your formula. In your case, that might result in a coarse temporal resolution which must not be bad, but if you want to increase temporal resolution under diffusive scaling (constant tau!) you have to increase spatial resolution in LBM.

Hope this helps.

Kind regards
Tim

[Author]

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