Spectra of spatial fluctuations in lattice gas cellular automata fluids

Abstract

Spectra or decay rates of spatial fluctuations for different Lattice Gas Cellular Automata (LGCA) Fluids are discussed using the Boltzmann equation. We demonstrate how the spectra provide information on the time and length scales of hydrodynamic behavior, isotropy and existence of spurious conservation laws in different LGCA models. The range of validity of generalized hydrodynamics with wave-number-dependent sound speed and transport coefficients is indicated. These properties give a quantitative explanation of several existing, but unexplained simulation results on the so called "negative bulk viscosities", and on the strong dispersion in the simulation results on sound damping. The use of the spectra to analyse the spatial instabilities occurring in certain models of LGCA is also indicated.