  In the gas kinetic theory, it showed that the zeroth order of the density
distribution function $f^{(0)}$ and local equilibrium density distribution
function were the Maxwellian distribution $f^{(eq)}(\rho,\emph{\textbf{u}}, T)$
with an external force term, where $\rho$ the fluid density,
$\emph{\textbf{u}}$ the physical velocity and $T$ the temperature, while in the
lattice Boltzmann equation (LBE) method numerous force treatments were proposed
with a discrete density distribution function $f_i$ apparently relaxed to a
given state $f^{(eq)}_i(\rho,\emph{\textbf{u}}^*)$, where the given velocity
$\emph{\textbf{u}}^*$ could be different with $\emph{\textbf{u}}$, and the
Chapman-Enskog analysis showed that $f^{(0)}_i$ and local equilibrium density
distribution function should be $f^{(eq)}_i(\rho,\emph{\textbf{u}}^*)$ in the
literature. In this paper, we start from the kinetic theory and show that the
$f^{(0)}_i$ and local equilibrium density distribution function in LBE should
obey the Maxwellian distribution $f^{(eq)}_i(\rho,\emph{\textbf{u}})$ with
$f_i$ relaxed to $f^{(eq)}_i(\rho,\emph{\textbf{u}}^*)$, which are consistent
with kinetic theory, then the general requirements for the force term are
derived, by which the correct hydrodynamic equations could be recovered at
Navier-Stokes level, and numerical results confirm our theoretical analysis.
