Boundary Conditions for Particle Based Hydrodynamics in Complex Flows

Particle based methods for the description of hydrodynamic or fluid phenomena have attracted much interest during the last decade. Methods like the Multi-Particle Collision Dynamics method [1] (MPCD) or the Direct Simulation Monte Carlo method [2] (DSMC) represent schemes which close the gap between a purely microscopic description of matter, characterised by force fields, and a macroscopic continuum description. The intermediate level, often referred to as mesoscopic scale, is thereby described on a coarser level. Methods are based on a pseudo-particle description where fluid properties within small volumes are described by discrete particles, thereby allowing for local fluctuations of mass, momentum, kinetic energy and particle density. Globally, conservation laws for mass, momentum, energy and particle number are fulfilled and effective interactions, modelled by stochastic collisions, between particles, are prescribed in such a way that even locally properties are conserved before and after an interaction step. Interactions are thereby described as binary(DSMC) or multi-particle (MPCD) collisions which are performed in so called collision-cells, into which particles are sorted in each simulation step and which have a volume to enclose O(10) particles. It has been demonstrated in various works that in the limit these methods can be reduced to the Boltzmann equation (for the case of DSMC) or to the Navier-Stokes equations (for the case of MPCD) and various hydrodynamic and fluid flow phenomena, have been reproduced with these methods. Hydrodynamic flows, like pressure driven Poiseuille flow or shear flow between parallel plates require proper boundary conditions in order to fulfil prescribed no-slip, partial-slip or slip conditions. Often, so called bounce back boundary conditions are applied in order to model no-slip conditions. It has been