CFD: 2D Lattice Boltzmann Method (LBM) for Peristaltic Pumping in Axisymmetric Vessel using MATLAB

I seek to first get a base code for the Lid-Driven Cavity problem using the Lattice Boltzmann Method (LBM) with a D2Q9 lattice and LBGK collision operator / Simple Relaxation Time (SRT) Model. I would need help to:

1. Understand the essential steps in creating this model, and to draw a schematic indicating the steps necessary to implement the boundary conditions.
2. Compare results to those found by Ghia et al in “High-Re solutions for incompressible
flow using the Navier-Stokes equations and a multigrid method.”
3. I would then like to numerically compute the spatial convergence rate of this scheme.
4. I also would like to examine the effect of relaxation time (Tau) and the Mach number on the method’s stability. I seek to understand how these parameters impact the feasible range of Reynolds numbers, required grid size and physical time step size.

After this base code is complete, I would like to create a simple 2D cylindrical vessel meshed manually in MATLAB. Use the LBM scheme created and verified using the steps prior to simulate peristaltic pumping in this axisymmetric vessel with a sinusoidal motion imposed on the vessel wall. Finally, visualize these flow results.

This has been done previously in 3D, and here I seek the most simple 2D form with simplifying assumptions. I can provide reference of the previous work in literature if necessary, and discuss more details if you are familiar with the LBM method, MATLAB, and CFD modeling, this should be a good medium-sized, time-sensitive project for you!