A Continuity Outlet Boundary Condition for the Lattice Boltzmann Method

A continuity outlet boundary condition for the Lattice Boltzmann Method (LBM) is proposed based on the assurance of the mass conservation of the system. The main advantage of the proposed boundary condition over the conventional Computational Fluid Dynamics (CFD) techniques is that the macroscopic properties, e.g. velocity, pressure etc. are not needed to be prescribed at the outlet, these properties are automatically calculated with the imposed boundary condition. This is especially useful in practice where the macroscopic properties at the outlet are difficult or impossible to be measured and described as in the biological flows. In order to test the feasibility of the proposed method, the LBM simulations are first verified for its capability to simulate flow in a symmetrically bifurcated channel. Then asymmetrically bifurcated geometries representing the blood vessels have been designed with different bifurcation angles. The new boundary condition is also tested for multi-component LBM simulations. For these cases, LBM predictions have been compared with the predictions for the commercial CFD software, namely ANSYS FLUENT at different Reynolds numbers. The results show that there is a good agreement between the LBM and FLUENT predictions, and this proves the capability of the proposed boundary condition as a viable method that can be used in practice.