  In this paper, a multiple-distribution-function lattice Boltzmann method
(MDF-LBM) with multiple-relaxation-time model is proposed for incompressible
Navier-Stokes equations (NSEs) which are considered as the coupled
convection-diffusion equations (CDEs). Through direct Taylor expansion
analysis, we show that the Navier-Stokes equations can be recovered correctly
from the present MDF-LBM, and additionally, it is also found that the velocity
and pressure can be directly computed through the zero and first-order moments
of distribution function. Then in the framework of present MDF-LBM, we develop
a locally computational scheme for the velocity gradient where the first-order
moment of the non-equilibrium distribution is used, this scheme is also
extended to calculate the velocity divergence, strain rate tensor, shear stress
and vorticity. Finally, we also conduct some simulations to test the MDF-LBM,
and find that the numerical results not only agree with some available
analytical and numerical solutions, but also have a second-order convergence
rate in space.
