I have gone through the article “Discrete lattice effects on the forcing term in the lattice Boltzmann method”. I am facing problems while implementing forcing term. I had successfully run matlab programs without forcing term. Where should I add the forcing term ? And how do I implement time step (delta t) in my program ?
I have made program in terms of lattice units not in the actual length. Please help me, what value of delta t should I take ?

Delta t in lattice units is usually set to 1. There are a lot of threads in this forum about the correct choice of lattice units. Please have a look there first.

Thanks a lot. Could you please refer me some threads where implementation of lattice units are there.
Also, I want to ask, while implementing forcing term (Gravity), how boundary conditions will change ?

The boundary conditions I am aware of do not change when you add a forcing term to the collision step.
Regarding useful threads dealing with lattice units: Just use the forum search and type “units”. You will find a lot of threads related to the topic. You just have to take some time to get an overview.

I think the time parameter in the force term is the “relaxation time”, you need to calculate the effect of the force in the velocity field and calculate Ueq and Veq, these terms are used to calculate Feq (Equilibrium distribution functions).
Ueq=U(I,J)+tawFx/Rho(I,J)
Veq=V(I,J)+tawFy/Rho(I,J)

Reference:
Sukop, “Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers”.

Shifting velocity method introduces the viscosity dependent results for macroscopic variables. Even it’s easier and actually is better in terms of stability, but it’s not recommended to be used.