The effect of stochastic correlations and fluctuations in the collision-coalescence process revisited: An algorithm for the numerical solution of the master equation and numerical results for realistic kernels

Generally, the modeling of size distribution in a collision-coalescence system is performed by the Smoluchowski or kinetic collection equation, which is a deterministic equation and has no stochastic correlations or fluctuations included. However, the full stochastic description of the growth of cloud particles in a coalescing system can be obtained from the solution of the master (or V- equation), which models the evolution of the state vector for the number of droplets of a given mass. Due to its complexity, only limited results were obtained for certain type of kernels (sum, product and constant kernels). In this work, a general algorithm for the solution of the master equation for stochastic coagulation was proposed. The performance of the method was checked by comparing the time evolution for the state probabilities with the analytical results obtained by other authors for a constant kernel. Fluctuations and correlations were calculated for the hydrodynamic kernel, and true stochastic averages obtained from the master equation were compared with numerical solutions of the kinetic collection equation for that case.