  In this paper, a multiple-distribution-function finite-difference lattice
Boltzmann method (MDF-FDLBM) is proposed for the convection-diffusion system
based incompressible Navier-Stokes equations (NSEs). By Chapman Enskog
analysis, the convection-diffusion system based incompressible NSEs can be
recovered from MDF-FDLBM. Some quantities, including the velocity gradient,
velocity divergence, strain rate tensor, shear stress and vorticity, can be
computed locally by the first-order moment of the non-equilibrium distribution
function. Through the von Neumann analysis, we conduct the stability analysis
for the MDF-FDLBM and incompressible finite-difference lattice Boltzmann method
(IFDLBM). It is found that the IFDLBM will be more stable than that of
MDF-FDLBM with small kinematic viscosity, and the MDF-FDLBM will be more stable
than that of IFDLBM with large Courant-Friedrichs-Lewy condition number.
Finally, some simulations are conducted to validate the MDF-FDLBM. The results
agree well with the analytical solutions and previous results. Through the
numerical testing, we find that the MDF-FDLBM has a second-order convergence
rate in space and time. The MDF-FDLBMcombined with non-uniform grid also works
well. Meanwhile, compared with IFDLBM, it can be found that MDF-FDLBM offers
higher accuracy and computational efficiency, reducing computation time by more
than 36%.
