Hi every body
consider a flow in channel. channel width is H. boundary condition is inlet pressure=Pi and outlet pressure Po.
Note that reynolds is unknown because we dont have any charactristic velocity.
if we consider charactristic length= H then delta_x=1/N(number of nodes). but my question is that How can I found delta_t to transfer unit from lattice to physical unit and vice versa???:((
If one BC was velocity it can be solved easily. For example if inlet=Ui we have:
taking U_charactristic-in-lattice=0.1 and U_charactristic= Ui ::::>> delta_t=U_charactristic-in-latticedelta_x
=========>>>> U=U_charactristicU_lattice(that we obtain it from solveing LBM)delta_x/delta_t=Ui0.1*delta_x/delta_t
As you see when velocity is known the unit transfer is easy but when we have pressure in inlet and outlet how we can transfer units???:(((((
thanks for your answer
Hi every body
nu_phys = (1/3)(tau-0.5)(dx^2/dt)
Assuming you know your physical viscosity, and lattice spacing, then you can use the equation to calculate timestep.
thank you very very much
but there is some problem
consider I use your proposed equation. if I consider e.g tau=1 then dt can be found. but how I can transfer pressure in real to lattice. you know that pressure dimension is:
now what about kg???
I really am confused. I read the notes of latt:
Choice of units in lattice Boltzmann simulations
but my problems remain:((((
thanks a lot
All the unit conversion factors are a combination of dx, dt and rho0, where,
rho_phys = rho_lb*rho0
Since we use rho_lb ~ 1, rho0 is simply the base density of your fluid.
Looking at the units of these factors we have,
dx = m, dt = s, rho0 = kg/m3,
And you need a conversion from dimless to kg/(m s^2), which would be,
Applying dimensional analysis on that you get,
(kg/m3)*(m2/dt2) = kg/m s2