Abstract
We demonstrate how three-dimensional fluid flow simulations can be carried out on the Cellular Automata Machine 8 (CAM-8), a special-purpose computer for cellular automata computations. The principal algorithmic innovation is the use of a lattice gas model with a 16-bit collision operator that is specially adapted to the machine architecture. It is shown how the collision rules can be optimized to obtain a low viscosity of the fluid. Predictions of the viscosity based on a Boltzmann approximation agree well with measurements of the viscosity made on CAM-8. Several test simulations of flows in simple geometries—channels, pipes, and a cubic array of spheres-are carried out. Measurements of average flux in these geometries compare well with theoretical predictions.
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References
S. Wolfram, ed.,Theory and Applications of Cellular Automata (World Scientific, Singapore, 1986).
T. Toffoli and N. Margolus,Cellular Automata Machines (MIT Press, Cambridge, Massachusetts 1987).
G. Weisbuch,Complex Systems Dynamics (Addison-Wesley Reading, Massachussetts, (1991).
U. Frisch, B. Hasslacher, and Y. Pomeau,Phys. Rev. Lett. 56:1505–1508 (1986).
U. Frisch, D. d'Humières, B. Hasslacher, P. Lallemand, Y. Pomeau, and J.-P. Rivet,Complex Systems 1:648 (1987).
D. H. Rothman,Geophysics 53:509–518 (1988).
A. J. C. Ladd and M. E. Colvin,Phys. Rev. Lett. 60:975–978 (1988).
M. Van der Hoef and D. Frenkel,Phys. Rev. 41:4277 (1990).
D. H. Rothman and J. Keller,J. Stat. Phys. 52:1119 (1988).
C. Appert and S. Zaleski,Phys. Rev. Lett. 64:1 (1990).
D. H. Rothman and S. Zaleski,Rev. of Mod. Phys. 66:1417–1479 (1994).
N. Margolus, T. Toffoli, and G. Vichniac,Phys. Rev. Lett. 56:1694–1697 (1986).
A. Clouqueur and D. d'Humières,Complex Systems 1:584–597 (1987).
D. d'Humières, P. Lallemand, and U. Frisch,Europhys. Lett. 2:291 (1986).
N. Margolus and T. Toffoli, Cellular-automata machines, inLattice-Gas Methods for Partial Differential Equations, in G. Doolen, ed. (Addison-Wesley, Reading, Massachusetts, 1990), pp. 219–249.
N. Margolus, Cam-8: A computer architecture based on cellular automata, inPattern Formation and Lattice-Gas Automata A. Lawniczak and R. Kapral, eds. (American Mathematical Society, Providence, Rhode Island, 1995).
M. Hénon,Complex Systems 1:475–494 (1987).
M. Hénon,Complex Systems 1:763–789 (1987).
M. Hénon, Optimization of collision rules in the FCHC lattice gas, and addition of rest particles, inDiscrete Kinetic Theory, Lattice-Gas Dynamics, and Foundations of Hydrodynamics, R. Monaco, ed. (World Scientific, Singapore, 1989), p. 146.
J. A. Somers and P. C. Rem, Obtaining numerical results from the 3D FCHC-lattice gas, inSpringer Proceedings on Physics, Workshop on Numerical Methods for the Simulation of Multi-Phase and Complex Flow (Springer-Verlag, Berlin, 1992), pp 59–78.
J. Hardy, O. de Pazzis, and Y. Pomeau,Phys. Rev. A 13:1949–1961 (1976).
G. D. Doolen, ed.,Lattice Gas Methods for Partial Differential Equations (Addison-Wesley, Reading, Massachusetts, 1991).
R. Cornubert, D. d'Humiéres, and D. Levermore,Physica D 47:241 (1991).
I. Ginzbourg and P. M. Adler,J. Phys. II France 4:191–214 (1994).
B. Ferréol and D. H. Rothman, Lattice-Boltzmann simulations of flow through Fontainebleau sandstone,Transport Porous Media, in press (1995).
B. Dubrulle, U. Frisch, M. Hénon, and J.-P. Rivet,J. Stat. Phys. 59: 1187–1226 (1990).
V. Coevorden, M. Ernst and J. Somers,J. Stat. Phys. 74:1085 (1994).
H. Hasimoto,J. Fluid Mech. 5:317 (1959).
A. S. Sangani and A. Acrivos,Int. J. Multiphase Flow 8:343 (1982).
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Adler, C., Boghosian, B., Flekkøy, E.G. et al. Simulating three-dimensional hydrodynamics on a cellular automata machine. J Stat Phys 81, 105–128 (1995). https://doi.org/10.1007/BF02179971
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DOI: https://doi.org/10.1007/BF02179971