Abstract
A class of lattice gas models are studied which are variants of the FCHC model. The aim is to achieve the highest possible Reynolds coefficient (inverse dimensionless viscosity) for efficient simulations of the three-dimensional incompressible Navier-Stokes equations. The models include an arbitrary number of rest particles and violation of semi-detailed balance. Within the framework of the Boltzmann approximation exact expressions are obtained for the Reynolds coefficients. The minimization of the viscosity is done by solving a Hitchcock-type optimization problem for the fine tuning of the collision rules. When the number of rest particles exceeds one, there is a range of densities at which the viscosity takes negative values. Various optimal models with up to 26 bits per node have been implemented on a CRAY-2 and their true transport coefficients have been measured with good accuracy. Fairly large discrepancies with Boltzmann values are observed when semi-detailed balance is violated; in particular, no negative viscosity is obtained. Still, the best model has a Reynolds coefficient of 13.5, twice that of the best previously implemented model, and thus is about 16 times more efficient computationally. Suggestions are made for further improvements. It is proposed to use models with very high Reynolds coefficients for sub-grid-scale modeling of turbulent flows.
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Dubrulle, B., Frisch, U., Hénon, M. et al. Low-viscosity lattice gases. J Stat Phys 59, 1187–1226 (1990). https://doi.org/10.1007/BF01334747
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DOI: https://doi.org/10.1007/BF01334747