A comparison between the bin and stochastic particle approach for the 1-D advection-condensation problem

In this presentation a comparison between the efficiency and accuracy of a particle code against a traditional bin model with respect to the 1-D advection-condensation problem will be illustrated. Because a particle model does not suffer from numerical errors associated with advection, both in space and across bins, the particle approach has a much smaller numerical error than the bin approach and as such will be used as our reference solution; however, the computational cost of a “true” particle model in which each particle represents one droplet is large and to offset this cost, with some loss in numerical accuracy, a stochastic particle model should be used. Thus, a key aspect of this presentation will be to demonstrate how many droplets can be represented by one particle in the stochastic approach to produce the same error for a given cost as was produced by the bin model. Because the approximations employed in the bin model break down as the grid resolution decreases, these comparisons will also be shown under grid refinement. Furthermore, to illustrate the role that turbulent or molecular diffusion plays, error versus cost comparisons using the two approaches will also be conducted under varying levels of explicit diffusion.