# Increase of velocity for Poiseuille Flow

Hi,

I’m simulating Poiseuille Flow with a d2q9 model and realized an increase of velocity of about 5 percent. So I wonder if this is due to mass increase which was often discussed in this forum. I don’t believe that my bounce back approach is wrong, since I use the simplest approach and the results seem to be quite reasonable. Furthermore I checked the code (Collision and Propagation-step) with Couette-Boundary-Conditions and I got the right results.

I implemented the Poiseuille-Condition as follows: at the inlet I set a specified velocity profile and at the outlet I set the density to 1 as basis for the calculation of my velocity profile. The unknown distributions at inlet and outlet are calculated due to the Zou/He approach with special treatment of the corner nodes.

With my d3q15 model I have similar effects what leads me to the conclusion that the code is working properly. Now I wonder if I can do something about that. Does someone of you has an idea?

Gamlastan

Hi,

could you describe on more detail what you see? Is the average velocity too large? Or do you see strange velocity distributions? What is your channel width? Are you sure that you have the correct channel diameter (typical question)? Do you reach steady state? What is your Mach number? etc., etc…

Timm

Hi Timm,

well the velocity profile seems to have reached steady state and looks like I expected it to be without any strange velocity distributions. Furthermore the dimension is right but just a bit too large. The dimensions of my gap are as follows:

gap-length (x-direction): 2.0 mm
gap-height (z-direction): 0.2 mm
Mach number: 0.0016
omega: 1.98
average velocity: 0.068 m/s
Re: 1.01
density: 900 kg/m^3
dyn. viscosity: 1.217 e-2 kg/(ms)

Maybe some values seem strange to you, but I can’t believe that the values are the source of the differences. Maybe Omega is a bit too high and I should reduce it by raising Mach number.

Gamlastan

How many lattice nodes do you have along the axes?

x-direction: 401
z-direcetion: 41

Hello,

I have just checked your time step and Mach number. Let’s see…
0.2mm corresponds to 40 lattice nodes, i.e. dx = 5e-6m
Your kinematic viscosity is 1.684e-3 in lattice units (from omega), and your physical viscosity is 1.352e-5 m^2/s (from viscosity and density)
I get a timestep like dt = 3.11e-9s which is quite small. Thus, dx/dt = 1607 m/s. For an average velocity of 0.068 m/s I get a Mach number of 4.23e-5 and not 0.0016.
Please write down how you have chosen the values for dx and dt, omega and so on. And please consider: The sound speed of your physical fluid does not need to match its correct value. Since the Mach number is not important in usual LBM simulations, its value can be set arbitrarily, as long as it is not large. This is NOT the case for the Reynolds number in general.

Timm

Hello Timm,

my calculation is based on the book “Molekulare Gasdynamik” by Hänel and a phd-thesis by Finck.
In this case one specifies a Mach-number and a reference-velocity and claculates out of this the speed of sound: cs = u/Ma.
Out of this one calculates a molecular velocity xi. xi = sqrt(3) * cs.
And dt follows: dt = dx/xi

finally Omega = dt *cs^2 / (nu + cs^2 * dt/2)

Gamlastan

This equation is correct, but I believe your result is not.