Mathematics
Scientific paper
Apr 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986phrvl..56.1505f&link_type=abstract
Physical Review Letters (ISSN 0031-9007), vol. 56, April 7, 1986, p. 1505-1508.
Mathematics
731
Digital Simulation, Gas Dynamics, Lattices (Mathematics), Navier-Stokes Equation, Thermodynamic Equilibrium, Boolean Functions, Field Theory (Physics), Massively Parallel Processors, Parallel Processing (Computers)
Scientific paper
It is shown that a class of deterministic lattice gases with discrete Boolean elements simulates the Navier-Stokes equations, and can be used to design simple, massively parallel computing machines. A hexagonal lattice gas (HLG) model consisting of a triangular lattice with hexagonal symmetry is developed, and is shown to lead to the two-dimensional Navier-Stokes equations. The three-dimensional formulation is obtained by a splitting method in which the nonlinear term in the three-dimensional Navier-Stokes equation is recasts as the sum of two terms, each containing spurious elements and each realizable on a different lattice. Freed slip and rigid boundary conditions are easily implemented. It is noted that lattice-gas models must be run at moderate Mach numbers to remain incompressible, and to avoid spurious high-order nonlinear terms. The model gives a concrete hydrodynamical example of how cellular automata can be used to simulate classical nonlinear fields.
Frisch Uriel
Hasslacher B.
Pomeau Yves
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