Time step across LBE-NS interface in coupling problem

Hi All,

I am working on a problem where I couple a Lattice Boltzmann solver (xFlows) with a Navier-Stokes (NS) solver. I have figured out the Lattice Units to dimensionless to physical units variable conversions required for LBE-NS interface data transfer. However, when I use the physical time step that I obtain from this conversion in my NS solver and run it for a lot of iterations, the flow does not seem to move at all in my NS domain. I used the same time step in my NS solver, which I obtain by converting lattice.deltaT() of xFlows into physical units using deltaT_{Phys} = deltaT_{dim}*l_ref_{Phys}/u_ref_{Phys}

{Phys} = physical units; {dim} = dimensionless units
l_ref_{Phys} = physical reference length
u_ref_{Phys} = physical reference velocity

I am simulating a 2D cylinder problem using this coupling. I use the cylinder2D example case of xFlows and just add a rectangular NS domain at the end of the LBE domain. Reynolds number = 100, hence it is an unsteady simulation. I am able to pass the flow variables across the interface without any problem.

Has anyone does this kind of simulation before? Could anyone please tell me how I can correctly link the time step in my NS simulation to that in my LBE simulation?

Thanks a lot!

I have also read the PhD Thesis and the Spatial Coupling paper (Computers and Fluids) of Dr. Latt which mentions LBE-NS coupling. A validation for Poiseuille flow was also shown. But the time step details are not mentioned in it. Are there more details of the formulation anywhere?