hello

I work with both but I experienced porous media only with NS. In both cases, you can add some extra forces to better model the fluid flow such as the drag force, the Forscheimer term... Both are strictly equivalent. NS equations may be recovered from LBM. The force terms are easily to implement in LBM. The main drawback is generally link quantities in lattice units to real values in real units.

State of the art engineering models for flow in porous media usually employ NS equations, or equations derived from them under extra assumptions (Darcy flow is a common model in reservoir and basin modelling for the oil industry, for example). This does not mean that LB does not work, only, that it has not become the industry standard yet.

The lattice Boltzmann equation is based on the Boltzmann equation, which is far more fundamental than the macroscopic equations, i.e., the Navier-Stokes equations. There are some advantages of the LBE in this case.

Hello,

I think both are interesting to be investigated. Actually, I have a project with one of my collaborators and a PhD student who will start working on the subject. Our aim is to compare LBE with the classical FV in presence of boundary layers. As mentioned in a previous comment, the LBE is more convenient in the microscopic scale. My understand is that both can be combined. 

I assume that you are modeling the two-phase flow. in that case, you are not going to understand the physical aspect of the flow by practicing LBM. because LBM is based on gas -kinetic theory and it is different from what we see in macroscopic world. the main idea of LBM is to model the Macroscopic flow by it's microscopic behavior and the microscopic world is not easy to describe. Unlike what our friend has shared above, i think  LBM is a powerful approach and it has a strong background to itself. it is not just a discretizing technique and it has it's own theory. to summarize, if you are interested in understanding the physics of the fluid, you better focus on the NS equations and understand  how they are derived.

Really: beginner, Non familiar with computational fluid dynamics, and you seek for a powerful approach in CFD, you search also for accuracy, coding simplicity (500 lines against thousands of lines for other methods FE, FV, FD). Here the LBM method offers the all, from microscopic to macroscopic with a clever background :)

I used it with phase-field model for solidification for modelling the fluid-flow in the melt. LBM is useful for me since I have moving boundaries and I need to apply parallel algorithms to speed up the simulation.