An Analysis of the Convergence of Stochastic Lagrangian/Eulerian Spray Simulations

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.