Particle-mesh schemes for advection dominated flows

Extended particle-in-cell (EPIC) schemes are considered with a view to applications in electrostatic drift-wave turbulence and ordinary hydrodynamical turbulence, where periodic boundary conditions are inappropiate. We treat issues relating to the dual particle-mesh representation and to the need to follow particle orbits accurately. A successful application of EPIC to an advection dominated flow is demonstrated. The errors are quantified so that choosing suitable numerical parameters to obtain a result of a given accuracy is straightforward. 30 refs., 4 figs., 2 tabs