A LATTICE BOLTZMANN SIMULATION OF FLUID FLOW IN POROUS MEDIA USING A MODIFIED BOUNDARY CONDITION

The lattice Boltzmann method has been considered as an effective method for the simulation of hydrodynamic flows. Handling the boundary condition accurately in simulation is extremely essential for a reliable study. In this paper, a multiple relaxation time lattice Boltzmann model with different boundary conditions was applied to mimic the flows in periodically symmetric and irregular structures. The scope of application and accuracy for different boundary conditions in various geometries was investigated. In addition, a hybrid boundary treatment method was introduced to simulate the non-Darcy flow in porous media, the simulation results of which were also compared to the results obtained using pressure boundary condition. The results show that for the symmetric and periodic flow simulation, both the body force and the pressure driven boundary treatments are perfectly equivalent and both can accurately capture the flow characteristics. While for the fluid flow in irregular structures, the body force and pressure boundary conditions are not equivalent, and the body force one has limited use and can only be applied to periodic structures. This implies that one must be cautious of the reliability of modeling when conducting model validation with simple structures. It seems that the regular structures could be inadequate to validate the modeling, which depends on the research issues, i.e., the flow patterns in what kinds of structures. Furthermore, the generalized periodic boundary condition proposed by previous authors combines periodic density momentum with a pressure gradient in one dimension is also not appropriate to conduct flow simulation in irregular models since this method ignores the effect of asymmetric obstacles in the direction perpendicular to the main streamlines. Moreover, the hybrid boundary condition can be used to perform flow simulations not only in periodic structures but also the irregular ones. In particular, for the inertial flow of fluids in porous media, the relatively high Reynolds number can be achieved readily with the hybrid boundary condition. For the pressure driven boundary condition, the pressure gradient comes from the density difference between the inlet and outlet. To provide a higher Reynolds number, it is necessary to implement a great density contrast in inlet and outlet nodes. However, this approach is inconsistent with physical situation and causes undesirable errors in simulation. All in all, the hybrid boundary condition has greater advantages over the pressure boundary condition.