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Derivation of the lattice Boltzmann method from the continuous kinetic theory [X. He and L. S. Luo, Phys. Rev. E 55, R6333 (1997); X. Shan and X. He, Phys. Rev. Lett. 80, 65 (1998)] is extended in order to obtain boundary conditions for the method. For the model of a diffusively reflecting moving solid wall, the boundary condition for the discrete set of(More)
A detailed treatment of the classical Chapman-Enskog derivation of hydrodynamics is given in the framework of Grad's moment equations. Grad's systems are considered as the minimal kinetic models where the Chapman-Enskog method can be studied exactly, thereby providing the basis to compare various approximations in extending the hydrodynamic description(More)
A new approach to the problem of reduced description for Boltzmann-type systems is developed. It involves a direct solution of two main problems: thermodynamici ty and dynamic invariance of reduced description. A universal construction is introduced, which gives a thermodynamic parameterization of an almost arbitrary approximation. Newton-type procedures of(More)
A new kinetic model for binary mixtures and its Lattice Boltzman (LB) discretiza-tion is presented. In the hydrodynamic limit the model recovers the Navier-Stokes and the Stefan-Maxwell binary diffusion equations. The thermodynamic consistency is ensured by the defined non-negative entropy production within the domain of applicability of the model. The(More)
In the last decade, minimal kinetic models, and primarily the Lattice Boltmann equation, have met with significant success in the simulation of complex hydrodynamic phenomena, ranging from slow flows in grossly irregular geometries to fully developed turbulence, to flows with dynamic phase transitions. Besides their practical value as efficient(More)