3D pulsatile flow with the lattice Boltzmann BGK method

We present detailed analysis of the accuracy of the lattice Boltzmann BGK method in simulating pulsatile flow in a 2D channel and a 3D tube. For the 2D oscillatory flow, we have observed a half time-steps shift between the theory and the simulation, that enhances the accuracy at least one order of magnitude. For 3D tube flow, we have tested the accuracy of the lattice Boltzmann BGK method in recovering the Womersley solution for pulsatile flow in a rigid tube with a sinusoidal pressure gradient. The obtained flow parameters have been compared to the analytical solutions. The influence of different boundary conditions such as the bounce-back and inlet-outlet boundary conditions on the accuracy was studied. Relative errors of the order of 0.001 in 2D with the bounce back on the nodes have been achieved. For the 3D simulations, it has been possible to reduce the error from 15% with the simple bounce-back to less than 5% with a curved boundary condition.