  This work derives how the convergence of stochastic Lagrangian/Eulerian
simulations depends on the number of computational parcels, particularly for
the case of spray modeling. A new, simple, formula is derived that can be used
for managing the numerical error in two or three dimensional computational
studies. For example, keeping the number of parcels per cell constant as the
mesh is refined yields an order one-half convergence rate in transient spray
simulations. First order convergence would require a doubling of the number of
parcels per cell when the cell size is halved. Second order convergence would
require increasing the number of parcels per cell by a factor of eight. The
results show that controlling statistical error requires dramatically larger
numbers of parcels than have typically been used, which explains why
convergence has been so elusive.
