Stochastic simulations as a benchmark for mathematical methods solving the coalescence equation

Common mathematical methods for the treatment of droplet coalescence attempt to approximate the coalescence equation in various manners. Some of these methods may yield different results when applied to realistic coalescence processes with complicated kernels. Thus, independent accuracy checks are desired. In this paper a modification of Gillespieʹs stochastic simulation algorithm is presented which yields reliable results at the price of an extensive CPU-time consumption. This algorithm is recommended to perform benchmark calculations to test the quality of faster methods for the numerical approximation of the coalescence equation. As examples for these approximation techniques a slightly modified discrete method of Kovetz and Olund and the integration scheme of Berry and Reinhardt are examined. Simulations carried out by the stochastic algorithm reveal that the integration scheme of Berry and Reinhardt is more accurate than the discrete method.