An efficient scheme for convection-dominated transport

Partial differential equations describing transport processes involving a significant effect of the flow velocity may be solved efficiently and easily, using a simple algorithm. The algorithm is based on the propagator(s) (or Green's functions) for the equations of transport theory. The numerical method employed is always at least as fast as finite differencing, and it reduces to a finite difference method in the short time-step limit, but is especially efficient in cases where flow dominates over diffusion and is consequently widely applicable in kinetic theory and fluid dynamics. Using this method, the ion distribution function and the potential in a plasma sheath were calculated in the presence of charge exchange collisions for a wide range of neutral densities.