  While accurate simulations of dense gas flows far from the equilibrium can be
achieved by Direct Simulation adapted to the Enskog equation, the significant
computational demand required for collisions appears as a major constraint. In
order to cope with that, an efficient yet accurate solution algorithm based on
the Fokker-Planck approximation of the Enskog equation is devised in this
paper; the approximation is very much associated with the Fokker-Planck model
derived from the Boltzmann equation [J. Comput. Phys., 229, 1077 (2010)]-[J.
Fluid Mech., 680, 574 (2011)]. The idea behind these Fokker-Planck descriptions
is to project the dynamics of discrete collisions implied by the molecular
encounters into a set of continuous Markovian processes subject to the drift
and diffusion. Thereby, the evolution of particles representing the governing
stochastic process becomes independent from each-other and thus very efficient
numerical schemes can be constructed. By close inspection of the Enskog
operator, it is observed that the dense gas effects contribute further to the
advection of molecular quantities. That motivates a modelling approach where
the dense gas corrections can be cast in the extra advection of particles.
Therefore, the corresponding Fokker-Planck approximation is derived such that
the evolution in the physical space accounts for the dense effects present in
the pressure, stress tensor and heat fluxes. Hence the consistency between the
devised Fokker-Planck approximation and the Enskog operator is shown for the
velocity moments up to the heat fluxes. For validation studies, a homogeneous
gas inside a box besides Fourier, Couette and lid-driven cavity flow setups are
considered. The results based on the Fokker-Planck model are compared with
respect to benchmark simulations, where good agreements are found for the flow
field along with the transport properties.
