Equation-Free Particle-Based Computations: Coarse Projective Integration   and Coarse Dynamic Renormalization in 2D
  Equation-free approaches have been proposed in recent years for the computational study of multiscale phenomena in engineering problems where evolution equations for the coarse-grained, system-level behavior are not explicitly available.   In this paper we study the dynamics of a diffusive particle system in a laminar shear flow, described by a two-dimensional Brownian motion; in particular, we perform coarse projective integration and demonstrate the particle-based computation of coarse self-similar and asymptotically self-similar solutions for this problem.   We use marginal and conditional Inverse Cumulative Distribution Functions (ICDFs) as the macroscopic observables of the evolving particle distribution. 
Yu Zou, Ioannis G. Kevrekidis, Roger G. Ghanem