A critical evaluation of force term in lattice Boltzmann method, natural convection problem

Few methods have been introduced and used in simulation fluid flows using lattice Boltzmann method (LBM) with external forces, such as buoyancy, surface tension, magnetic, etc. In some problems, the external force is constant, for instance gravitational force with constant density flows, while for other problems the force may vary spatially and/or temporally with non-zero gradients, such as gravitational force with variable density flows. For problems with the variable force term, adding force term to LBM may not be trivial. The paper evaluates mainly three different schemes of adding force term to LBM with BGK method. In this work, natural convection in a closed and an open ended cavities were used as a test platform. The results for the differentially heated cavity are introduced first. For the open cavity, the vertical left hand wall of the cavity is heated and opposing side is opened to the ambient, with other connecting boundaries are assumed to be adiabatic. Prior to the solution, the boundary conditions at the opening are unknown. The results of predictions using LBM are compared with results predicted by using finite volume method (FVM). The results are presented for Ra=106 and for Pr=0.71. It is found that most methods suggested in the literature produces similar results, despite that some authors claim that their scheme is more accurate than the other schemes.