Mesoscopic fluids continuum models

The lattice Boltzmann method is a mesoscopic simulation method for complex fluid systems. The fluid is modeled as fictitious particles, and they propagate and coUide over a discrete lattice domain at discrete time steps. Macroscopic continuum equations can be obtained from this propagation-colhsion dynamics through a mathematical analysis. The particulate nature and local d3mamics also provide advantages for complex boundaries, multiphase/multicomponent flows, and parallel computation. 

The simplest way to conduct the simulations of mesoscopic phenomena, consists in down-scaling of the continuum approach or upscaling (or coarse graining) the particle model. The limitation of the first approach is determined by the granular properties of matter, which are revealed for very small system. The behavior of granular fluid is different from that in the bulk. For example, very small systems may exhibit solid-liquid coexistence over a range of temperature different than that for large systems [31]. However, new approaches such as ... 

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