Ideal pressure term for non ideal fluid LBM simulation

Dear All participant of this forum

I am simulating a planar couette flow in LBM. The study is on the shear banding of colloidal glass. I have osmotic pressure
as a driving force and i have multiplied it with a prefactor to make it in the LBM unit.

I read from a book that LBM by itself has ideal pressure (i.e rho*cs_2) in it and one has to subtract this term from the applied pressure during implementation. In my simulation i had subtracted this term but i found it is so big and keep on increasing the density in my simulation.

Is there any one here who has experience in simulating non ideal fluid?

Thanks

Addis

Hello!I am a begginer about LBM.I am comfused about ideal pressure (i.e rho*cs_2) in LBM.I do not know how to convert it to macro pressure.And you say that "one has to subtract this term from the applied pressure during implementation."So I want to know which is the book?
Best wishes for you!