Comparison of accuracy and efficiency between the lattice Boltzmann method and the finite difference method in viscous/thermal fluid flows

The accuracy and efficiency of the lattice Boltzmann method (LBM) and the finite difference method (FDM) are numerically investigated. In the FDM for incompressible viscous flows, it is usually needed to solve a Poisson equation for the pressure by iteration or relaxation technique, while in the LBM, such special treatment is not required. Two-dimensional problems of incompressible viscous flows and thermal fluid flows are computed by using the LBM and FDM. In the problem of flows through a porous structure, the present results indicate that the LBM is more efficient than the FDM, because there is no need to relax the pressure fields in the LBM at relatively high Reynolds numbers. Therefore, it is found that the LBM is useful for the investigation of transport phenomena in complex geometries such as porous structures.