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Some Recent Results on Discrete Velocity Model and Ramifications for Lattice Boltzmann Equation
Some rigorous results on discrete velocity models are briefly reviewed and their ramifications for the lattice Boltzmann equation (LBE) are discussed. In particular, issues related to thermodynamics and H-theorem of the lattice Boltzmann equation are addressed. It is argued that for the lattice Boltzmann equation satisfying the correct hydrodynamic equations, there cannot exist an H-theorem. Nevertheless, the equilibrium distribution function of the lattice Boltzmann equation can closely approximate the genuine equilibrium which minimizes the H-function of the corresponding continuous Boltzmann equation. It is also pointed out that the equilibrium in the LBE models is an attractor rather than a true equilibrium in the rigorous sense of H-theorem. Since there is no H-theorem to guarantee the stability of the LBE models at the attractor, the stability of the attractor can only be studied by means other than proving an H-function.
Li shi zhi ren shi
None
Li Shi Min, Founding the Tang Dynasty
Li Shi Min was a man of great political and military accomplishments, narrated here with the battle stratagems and clever counsel that carried him forward. This book tells how he helped his father Li Yuan to establish the Tang Dynasty and the contributions he made to unifying China. Author Hung Hing Ming draws on China's historical records and chronicles to recount the battles to conquer the warlords and local strongmen in different parts of China, the wise policies he adopted, and the means by which he inspired officials to put forward good suggestions. His deeds, policies and constructive interactions with his ministers and generals were compiled into guides and teaching materials for successors to the Chinese throne. Much of this leadership training advice is still useful today. This book will be an asset to readers as there are few works in English that introduce these cultural motifs that color the thinking of nation so important to ours.
Theory of the Lattice Boltzmann Method: Lattice Boltzmann Models for Non-ideal Gases
In this paper a procedure for systematic a priori derivation of the lattice Boltzmann models for non-ideal gases from the Enskog equation (the modified Boltzmann equation for dense gases) is presented. This treatment provides a unified theory of lattice Boltzmann models for non-ideal gases. The lattice Boltzmann equation is systematically obtained by discretizing the Enskog equation in phase space and time. The lattice Boltzmann model derived in this paper is thermodynamically consistent up to the order of discretization error. Existing lattice Boltzmann models for non-ideal gases are analyzed and compared in detail. Evaluation of these models are made in light of the general procedure to construct the lattice Boltzmann model for non-ideal gases presented in this work.
Li shi zhi ren shi
None
Yi Da Li Luo Man Shi
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