Mass Modified Outlet Boundary for a Fully Developed Flow in the Lattice Boltzmann Equation

Outlet boundary conditions for fully developed flow are discussed for a two-dimensional lattice Boltzmann BGK model (LBGK), and most of the existing ones are found to be incapable of ensuring mass conservation of the whole flow field. Based on this analysis, a mass modified outlet boundary is proposed, which can completely overcome this shortcoming. Tests were done against a two-dimensional plane channel flow and flow over a backward-facing step. The results show that the present method is of good accuracy, stability, and fast convergence, especially for relatively high relaxation time and relatively small lattice number. It can improve the accuracy of the numerical results as well as save the computational time.

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