7,220 research outputs found
Renormalized Equilibria of a Schloegl Model Lattice Gas
A lattice gas model for Schloegl's second chemical reaction is described and
analyzed. Because the lattice gas does not obey a semi-detailed-balance
condition, the equilibria are non-Gibbsian. In spite of this, a self-consistent
set of equations for the exact homogeneous equilibria are described, using a
generalized cluster-expansion scheme. These equations are solved in the
two-particle BBGKY approximation, and the results are compared to numerical
experiment. It is found that this approximation describes the equilibria far
more accurately than the Boltzmann approximation. It is also found, however,
that spurious solutions to the equilibrium equations appear which can only be
removed by including effects due to three-particle correlations.Comment: 21 pages, REVTe
A lattice Boltzmann model for natural convection in cavities
We study a multiple relaxation time lattice Boltzmann model for natural convection with moment–based boundary conditions. The unknown primary variables of the algorithm at a boundary are found by imposing conditions directly upon hydrodynamic moments, which are then translated into conditions for the discrete velocity distribution functions. The method is formulated so that it is consistent with the second–order implementation of the discrete velocity Boltzmann equations for fluid flow and temperature. Natural convection in square cavities is studied for Rayleigh numbers ranging from 103 to 106. An excellent agreement with benchmark data is observed and the flow fields are shown to converge with second order accuracy
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