Hydrodynamic Shock Wave Studies within a Kinetic Monte Carlo Approach
  Kinetic approaches are routinely employed to simulate the dynamics of systems that are too rarified to be described by the Navier-Stokes equations. However, generally they are far too computationally expensive to be applied for systems that are governed by continuum hydrodynamics. In this paper, we introduce a massively parallelized test-particle based kinetic Monte Carlo code that is capable of modeling the phase space evolution of an arbitrarily sized system that is free to move in and out of the continuum limit. Using particle mean free paths which are small with respect to the characteristic length scale of the simulated system, we retrieve continuum behavior, while non-equilibrium effects are observed when the mean free path is increased. To demonstrate the ability of our code to reproduce hydrodynamic solutions, we apply a test-suite of classic hydrodynamic shock problems. Simulations using tens of millions of test-particles are found to reproduce the analytical solutions well. 
Irina Sagert, Dirk Colbry, Terrance Strother, Rodney Pickett, Wolfgang   Bauer
physics.flu-dyn astro-ph.IM