Lattice gas hydrodynamics in two and three dimensions

Conference · Wed Jan 01 04:00:00 EST 1986

OSTI ID:6063731

Frisch, U; d'Humieres, D; Hasslacher, B; Lallemand, P; Pomeau, Y; Rivet, J P

Hydrodynamical phenomena can be simulated by discrete lattice gas models obeing cellular automata rules (U. Frisch, B. Hasslacher, and Y. Pomeau, Phys. Rev. Lett. 56, 1505, (1986); D. d'Humieres, P. Lallemand, and U. Frisch, Europhys. Lett. 2, 291, (1986)). It is here shown for a class of D-dimensional lattice gas models how the macrodynamical (large-scale) equations for the densities of microscopically conserved quantities can be systematically derived from the underlying exact ''microdynamical'' Boolean equations. With suitable restrictions on the crystallographic symmetries of the lattice and after proper limits are taken, various standard fluid dynamical equations are obtained, including the incompressible Navier-Stokes equations in two and three dimensions. The transport coefficients appearing in the macrodynamical equations are obtained using variants of fluctuation-dissipation and Boltzmann formalisms adapted to fully discrete situations.

• Research Organization: Los Alamos National Lab., NM (USA); Observatoire de Nice, 06 (France); Ecole Normale Superieure, 75 - Paris (France)
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 6063731
• Report Number(s): LA-UR-87-2524; CONF-8610281-2; ON: DE87013167
• Country of Publication: United States
• Language: English

Related Subjects

640410* -- Fluid Physics-- General Fluid Dynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOLTZMANN EQUATION
CRYSTAL LATTICES
CRYSTAL STRUCTURE
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE DIFFERENCE METHOD
FLUCTUATIONS
FLUID FLOW
FLUID MECHANICS
GAS FLOW
HYDRODYNAMICS
INCOMPRESSIBLE FLOW
ITERATIVE METHODS
MECHANICS
NAVIER-STOKES EQUATIONS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PROBABILISTIC ESTIMATION
REYNOLDS NUMBER
STURM-LIOUVILLE EQUATION
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS
VARIATIONS
VISCOSITY