Shan, Xiaowen; Yuan, Xue-Feng; Chen, Hudong Kinetic theory representation of hydrodynamics: a way beyond the Navier-Stokes equation. (English) Zbl 1097.76061 J. Fluid Mech. 550, 413-441 (2006). Summary: We present in detail a theoretical framework for representing hydrodynamic systems through a systematic discretization of the Boltzmann kinetic equation. The work is an extension of a previously proposed formulation [X. Shan and X. He, Phys. Rev. Lett. 80, 65 ff (1998)]. Conventional lattice Boltzmann models can be shown to be directly derivable from this systematic approach. Furthermore, we provide here a clear and rigorous procedure for obtaining higher-order approximations to the continuum Boltzmann equation. The resulting macroscopic moment equations at each level of the systematic discretization give rise to the Navier-Stokes hydrodynamics and those beyond. In addition, theoretical indications to the order of accuracy requirements are given for each discrete approximation, for thermohydrodynamic systems, and for fluid systems involving long-range interactions. All these are important for complex and micro-scale flows and are missing in the conventional Navier-Stokes order descriptions. The resulting discrete Boltzmann models are based on a kinetic representation of the fluid dynamics, hence the drawbacks in conventional higher-order hydrodynamic formulations can be avoided. Cited in 160 Documents MSC: 76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics 76A02 Foundations of fluid mechanics 82D15 Statistical mechanics of liquids Keywords:higher-order approximations; discrete Boltzmann models PDF BibTeX XML Cite \textit{X. Shan} et al., J. Fluid Mech. 550, 413--441 (2006; Zbl 1097.76061) Full Text: DOI OpenURL