Lattice Boltzmann modelling of pulsatile flow using moment boundary condiitons

A Lattice Boltzmann Method (LBM) with moment based boundary conditions is used to numerically simulate the two-dimensional flow between parallel plates, driven by a pulsating pressure gradient. The flow is simulated by using a single relaxation time model under both non-slip and Navier-slip boundary conditions. Convergence is investigated by using two distinct approaches. The first approach uses acoustic scaling in which we fix Mach, Reynolds and Womersley numbers whilst varying the LBM relaxation time. Diffusive scaling is used in the second approach - here we fix the Reynolds and Womersley numbers and the relaxation time whilst the Mach number decreases with increasing grid size. For no-slip conditions using acoustic scaling, the numerical method converges, but not always to the appropriate analytical result. However, the diffusive scaling approach performs as expected in this case, showing second-order convergence to the correct analytical result. Convergence to the analytical solution (though not always second-order) is also observed for the simulations with Navier-slip using acoustic scaling