Consistent Forcing Scheme in the Simplified Lattice Boltzmann Method for Incompressible Flows (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 proposea consistent forcing scheme in SLBM for incompressible flows with external forces. Thelattice discrete effects are considered at the level of distribution functions in the presentforcing scheme. Consequently, it is more accurate compared with the original forcingscheme 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 resolvedthrough 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- andtime-dependent body forces. Hence, the present forcing scheme overcomes the disadvantages of the original forcing scheme and the body force can be accurately imposedin the present scheme even when a coarse mesh is applied while the original schemefails. Excellent agreements between the analytical solutions and our numerical resultscan be observed.
Keywords: Simplified lattice Boltzmann method; force term implementation; non-uniform body force; ChapmanEnskog analysis; the discrete effect.