Consistent inflow and outflow boundary conditions for transported probability density function methods

In transported probability density function (PDF) methods, the PDF transport equations are most often solved with realization based techniques using particles. In this paper, a consistent treatment of particle in- and outflow boundary conditions for transported PDF methods is devised. It is shown that the presented approach is simple and, most important, consistent with the underlying Eulerian PDF transport equation. This is not the case for other boundary condition implementations discussed in the literature, especially if the fluctuating particle velocities are high compared with the averaged ones.