As a newbie to the lattice-boltzmann method I have problems with unit conversions as well. That’s why I’d like to present an example here the way I’d like to do the conversion and ask if this way of conversion is correct.
Let’s say I’d like to compute a solution for the lid-driven cavity flow of a cavity with dimensions 1m x 1m x 1m and a velocity of 10 m/s on top of the cavity.
–> l_0,p = 1 m ( reference length in physical units )
–> u_0,p = 10 m / s ( reference velocity in physical units )
As proposed in Jonas Latt’s article on unit conversion I set the boundary velocity u_0,lb = 0.02 in the LBM simlulation.
–> u_0,lb = 0.02 ( reference velocity in lattice-boltzmann units )
Further I set the number of grid points to 100 per dimension yielding a 100 x 100 x 100 grid with 100 * 100 * 100 grid points in total. This yields
–> dx = 1 / 100
u_0,lb = dt / dx (see J.Latt - reference velocity in lattice-boltzmann units)
dt = dx * u_0,lb = 1/100 * 0.02 = 0.0002
From my boundary conditions I know that the physical reference time
t_0 = l_0 / u_0 = 1 m / 10 m/s = 0.1 s
Thus I need
N_iter = 1 / dt = 5000
steps to simulate 0.1 seconds of the fluid flow.
Is this correct?