  A numerically stable method to solve the discretized Boltzmann-Enskog
equation describing the behavior of non ideal fluids under inhomogeneous
conditions is presented. The algorithm employed uses a Lagrangian
finite-difference scheme for the treatment of the convective term and a forcing
term to account for the molecular repulsion together with a
Bhatnagar-Gross-Krook relaxation term. In order to eliminate the spurious
currents induced by the numerical discretization procedure, we use a
trapezoidal rule for the time integration together with a version of the
two-distribution method of He et al. (J. Comp. Phys 152, 642 (1999)). Numerical
tests show that, in the case of one component fluid in the presence of a
spherical potential well, the proposed method reduces the numerical error by
several orders of magnitude. We conduct another test by considering the flow of
a two component fluid in a channel with a bottleneck and provide information
about the density and velocity field in this structured geometry.
