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An H-Theorem for the Lattice Boltzmann Approach to Hydrodynamics | | Alexander J. Wagner
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5 Aug 1998 | | Subject: | Statistical Mechanics; Soft Condensed Matter; Cellular Automata and Lattice Gases | cond-mat.stat-mech comp-gas cond-mat.soft nlin.CG | | Abstract: | The lattice Boltzmann equation can be viewed as a discretization of the continuous Boltzmann equation. Because of this connection it has long been speculated that lattice Boltzmann algorithms might obey an H-theorem. In this letter we prove that usual nine-velocity models do not obey an H-theorem but models that do obey an H-theorem can be constructed. We consider the general conditions a lattice Boltzmann scheme must satisfy in order to obey an H-theorem and show why on a lattice, unlike the continuous case, dynamics that decrease an H-functional do not necessarily lead to a unique ground state. | | Source: | arXiv, cond-mat/9808052 | | Services: | Forum | Review | PDF | Favorites | |
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