Choosing delX and delT

Hi All,

I am trying to reproduce a thin film lubrication problem in a plane slider with the following characteristics.

Everything is in physical units.

L - Length of the channel
h0 - smaller width
h1 - larger width
rho - density
mu - viscocity
cs - speed of sound

I am trying to proceed as follows…

nu = mu/rho (Kinematic Viscocity)

I am planning to use Nx lattice nodes in x-direction

delX = L / Nx
delT = (1/sqrt(3))*(delX / cs)

tau = 0.5*(1+6nudelT/delX^2)

For a given lattice speed, to increase the value of tau, I make the grid finer (i.e. choose a larger value for Nx)

Ny = (h1/delX) + 2

c = delX/delT

In this way I am neither converting into lattice units nor non-dimensionalising.

Please correct me if I am making a mistake