(untitled) (Communications in Computational Physics, 2021)
Considering the fact that the lattice discrete effects are neglected while introducing a body force into the simplified lattice Boltzmann method (SLBM), we propose a consistent forcing scheme in SLBM for incompressible flows with external forces. The lattice discrete effects are considered at the level of distribution functions in the present forcing scheme. Consequently, it is more accurate compared with the original forcing scheme used in SLBM. Through Taylor series expansion and Chapman-Enskog (CE) expansion analysis, the present forcing scheme can be proven to recover the macroscopic Navier-Stokes (N-S) equations. Then, the macroscopic equations are resolved through a fractional step technique. Furthermore, the material derivative term is discretized by the central difference method. To verify the results of the present scheme, we simulate with multiple forms of external force interactions including the space- and time-dependent body forces. Hence, the present forcing scheme overcomes the disadvantages of the original forcing scheme and the body force can be accurately imposed in the present scheme even when a coarse mesh is applied while the original scheme fails. Excellent agreements between the analytical solutions and our numerical results can be observed.