Cell Size Error in Stochastic Particle Methods for Coagulation Equations with Advection

The error arising from the delocalization of the coagulation interaction in stochastic particle methods is studied. The model under consideration includes advection, coagulation, and inception. Stochastic particle methods depend on several discretization parameters, due to the finite number of particles, the decoupling of transport and interaction (time step), and the spatial delocalization of the interaction (cell size). The paper studies the dependence on the cell size of the steady state solution obtained in the infinite-particle-number limit. Sufficient conditions for second order approximation are provided. Examples are given, where only first order approximation is observed