Thermal transport properties in a square lattice gas

Abstract

Explicit expressions are derived for thermal transport coefficients (heat conductivity, viscosities) L(ϱ, β) as a function of density and temperature for a cellular automaton fluid with nontrivial energy conservation and a physically meaningful definition of temperature. The functions L(ϱ, β) are studied analytically and numerically, using mean field theory. They show nonanalytic and scaling behavior at low temperature in the neighborhood of special densities. We also study the staggered diffusivities arising from spuriously conserved quantities in lattice gases. As a square lattice does not have the isotropic symmetry of a fluid we explore the ways of implementing isotropy at the level of the nonlinear Navier-Stokes equation.