  A grid-free variant of the Direct Simulation Monte Carlo (DSMC) method is
proposed, named the Isotropic DSMC (I-DSMC) method, that is suitable for
simulating dense fluid flows at molecular scales. The I-DSMC algorithm
eliminates all grid artifacts from the traditional DSMC algorithm; it is
Galilean invariant and microscopically isotropic. The stochastic collision
rules in I-DSMC are modified to yield a non-ideal structure factor that gives
consistent compressibility, as first proposed in [Phys. Rev. Lett. 101:075902
(2008)]. The resulting Stochastic Hard Sphere Dynamics (SHSD) fluid is
empirically shown to be thermodynamically identical to a deterministic
Hamiltonian system of penetrable spheres interacting with a linear core pair
potential, well-described by the hypernetted chain (HNC) approximation. We
apply a stochastic Enskog kinetic theory for the SHSD fluid to obtain estimates
for the transport coefficients that are in excellent agreement with particle
simulations over a wide range of densities and collision rates. The fluctuating
hydrodynamic behavior of the SHSD fluid is verified by comparing its dynamic
structure factor against theory based on the Landau-Lifshitz Navier-Stokes
equations. We also study the Brownian motion of a nano-particle suspended in an
SHSD fluid and find a long-time power-law tail in its velocity autocorrelation
function consistent with hydrodynamic theory and molecular dynamics
calculations.
