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Mesoscopic

Mesoscopic methods operate on length and time scales between the particle and continuum levels. For this reason, they combine elements of particle-based dynamics and continuum hydrodynamics.

An example is the lattice Boltzmann method, which models a fluid as a collection of fictitious particles that exist on a lattice. The particles evolve in time through streaming (straight-line motion) and collisions. Conceptually, it is based on the Boltzmann equation for dilute gases, where the dynamics of a molecule consists of free motion interrupted by discrete binary collisions, but it is also applied to liquids. Despite the analogy with individual molecular trajectories, it is a coarse-grained description that typically operates on length and time scales larger than those of true molecular dynamics (hence the notion of "fictitious" particles).

Other methods that combine elements of continuum and particle-level dynamics include smoothed-particle hydrodynamics, dissipative particle dynamics, and multiparticle collision dynamics.