# The lower limit for LB's density

Hello everyone,
In my model, I try to apply the pressure difference between inlet and outlet by applying difference rho for inlet and outlet. As I understand, LB’ density equals to rho_lb=rho_p/rho0. If the fluid is incompressible, rhoLB will always be 1.
Therefore , rho_lb inlet = 1 and rho _lb outlet = 1 - delta(rho_lb); where delta(rho_lb) = (3deltaPu_lb^2)/(rho_p*u_p^2)
I know that delta(rho_lb) cannot larger than 1, but I am not sure what is the maximum value that delta(rho_lb) can reach, i.e what is the lower limit for the LB’s density ?

Also, my relaxation time in my model is very close to 0.5, e.g 0.5008, that might be the reason cause the instability in my model. Besides increasing the lattice resolution which increases the running time, and using MRT, is there any method to solve this problem?
Thank you for your time

Hi Michelle,

sorry for the delay in replying, tau = 0.5008 is very small, firstly try to change it if you have instability problems. Try with tau > 1…this will also speed up the simulation because if uLB is fixed increasing tau means to increase the timestep. Also, check to have uLB < 0.4. If this doesn’t work I think the next step is to increase the grid resolution.

Cheers,

mars

Hi Mars;
Thank you for replying my question. My problem is that I want to apply a range of pressure difference between inlet and outlet. When I increase my relaxation time, it also increase my delta LB rho, therefore, my rhoLB at outlet can be very small or negative. Could you please suggest me how to solve this problem ? Or any articles that I can look for.
Thank you very much. I am the only one who work on this topic in my uni, so I have no one to approach. Having the support from you guys is helpful to me.