Optimal time step length for Lagrangian, interacting-particle simulations of diffusive mixing

To date, Lagrangian mass-transfer-based interacting particle methods have been shown to be rigorous and capable of modeling a diverse range of so- phisticated problems but have lacked formal criteria for choosing an optimal time step length (t). In Eulerian (grid-based) methods, a user can typically reduce t to an arbitrary level and expect to see corresponding gains in accuracy. The particle methods that we consider behave similarly, but only up to a point: for a fixed number of particles, t can become so small that the magnitude of diffu- sion restricts particles from communicating via mass-transfer, and at this point solution accuracy begins to degrade. In this work, we formalize criteria for deter- mining when this transition takes place, based on the properties of a particular system, and we use this criteria to choose the optimal t. We test these results with numerical experiments that demonstrate accurate prediction of the optimal t for a variety of conditions.