Hello,
I only have started to study LBM. However I solved Navies-Stokes equations + heat exchange + chemistry for practical 3-D tasks during 15-20 years using method of finite volumes. And I never wrote so-called dimensionless form of equations. All functions, equations, coefficients, nodes of grids and so on I expressed in SI-units (m, kg, sec, N, J, W). Reynolds’s number can be calculated after calculations if it is necessary for reports or papers. So it is more convenient to do debugging of the code since we do not lose physical sense of all expressions. Can I act so in LB method?
Whether you prefer to talk about your model in dimensionless variables or in SI units is of course completely up to you. In numerical simulation, consider the dimensionless system as just another system of units which is more convenient to discuss numerics, whereas SI is more convenient in many areas of engineering. But they are related to each other by simple conversion factors, and this is really no big deal.
What matters is that your LB simulation runs in lattice units. And you should be aware of how you converted any single parameter and variable from the system of your choice to lattice units. The tutorial on conversion rules to lattice units contains a few basic observations which should help you out. The document introduces dimensionless variables, but feel free to ignore that part. More precisely, skip the beginning where the physical equation is converted to dimensionless ones. Then, replace all occurrences of “dimensionless system/variables” by “SI units”. This should pretty much do it.
But I certainly recommend that you take a little time to understand what the dimensionless form of the equations is about. On one hand, this abstraction helps getting a more fundamental understanding of your physical model. It clarifies for example on how many parameters the equation really depends and prevents you from fiddling around with a random amount of parameters. On the other hand it makes it easier to communicate with a partner who is not familiar with your particular lab setting. And let’s be honest: to have a vague understanding of what your simulation is doing, you certainly want to know the Reynolds number before writing the report, don’t you?