CoChat
Sign Up
Cited by 2,788Cellular Automata and ApplicationsLattice Boltzmann Simulation StudiesComputer Graphics and Visualization Techniques

Lattice-gas automata for the Navier-Stokes equation

Open access
Frisch, U., Hasslacher, B., Pomeau, Y.·1986·Physical Review Letters
DOI 10.1103/physrevlett.56.1505
Open this paper in CoChat — free accountOpen PDF

Abstract

~e show that a class of deterministic lattice gases with discrete Boolean elements simulates the Navier-Stokes equation, and can be used to design simple, massively parallel computing machines.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1103/physrevlett.56.1505

Cites

11 of 11 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

Research works printed but not linked: 17

  1. [1]1. J. L. Oneto, S. A. Orszag, J. P. Rivet, T. Shimomura, Z. S. She, B. Shraiman, T. Toffoli, and G. Vichniac, as well as the following: Woods Hole Geophysical Fluid Dynamics Summer Program (U.F. , Y.P. ); Aspen Center for Physics, 1985 Chaos Workshop (B.H.); and Service de Physique Theorique, Centre d'Etudes Nu- cleaires de Saclay (B.H.). This work was supported in part by National Science Foundation Grant No. 8442384. tU. Frisch, Phys. Scr. T9, 131 (1985).
  2. [2]2. E. Knuth, The Art ofComputer Programming: Semi Nu merical Algorithms (Addison-Wesley, Reading, Mass. , 1981), Vol. 2, p. 238.
  3. [4]4. S. Wolfram, Nature 311, 419 (1984).
  4. [5]5. 4Y. Pomeau, J. Phys. A 17, L415 (1984);
  5. [8]8. sJ. C. Maxwell, The Scientific Papers, Vol 2(Ca.mbridge Univ. Press, Cambridge, England, 1890), p. 681.
  6. [9]9. 6G. E. Uhlenbeck and G. W. Ford, Lectures in Statistical Mechanics, Lectures in Applied Math Vol. 1 (American Mathematical Society, Providence, R.I. , 1963).
  7. [10]10. tJ. E. Broadwell, Phys. Fluids 7, 1243 (1964);
  8. [11]11. R. Gatig- nol, Theoric Cinetique des Gaz a Repartition Discrete des Vitesses, Lecture Notes in Physics Vol. 36 (Springer, Berlin, 1975).
  9. [12]12. sJ. Hardy and Y. Pomeau, J. Math. Phys. 13, 1042 (1972);
  10. [13]13. J. Hardy, Y. Pomeau, and O. de Pazzis, J. Math. Phys. 14, 1746 (1973);
  11. [14]14. J. Hardy, O. de Pazzis, and Y. Pomeau, Phys. Rev. A 13, 1949 (1976).
  12. [15]15. Forster, D. R. Nelson, and M. J. Stephen, Phys. Rev. A 16, 732 (1977).
  13. [16]16. taS. Harris, Phys. Fluids 9, 1328 (1966).
  14. [17]17. U. Frisch, B. Hasslacher, and Y. Pomeau, "Hydro- dynamics on Lattice Gases, " to be published. &2J. Rivet and U. Frisch, C.R. Seances Acad. Sci. , Ser. 2 302, 267 (1986).
  15. [19]19. t4A. N. Kolmogorov, C.R. (Dokl. ) Acad. Sci. USSR 30, 301, 538 (1941);
  16. [20]20. R. Kraichnan, Phys. Fluids 10, 1417 (1967);
  17. [21]21. G. K. Batchelor, Phys. Fluids 12, Suppl. 2, 233 (1969).

Cited by

Sorted by citations

Related

Authors
Frisch, U., Hasslacher, B., & Pomeau, Y.
Affiliations
Centre National de la Recherche Scientifique (FR)
ORCID
Frisch, U.
Venue
Physical Review Letters
Publisher
American Physical Society (APS)
Published
1986-04-07
Volume
56
Issue
14
Pages
1505-1508
ISSN
0031-9007 (ISSN-L)
DOI
10.1103/physrevlett.56.1505
OpenAlex
W2014786311
Cited by
2,788
References
11
Citations by year
2026: 42 · 2025: 48 · 2024: 46 · 2023: 58 · 2022: 51 · 2021: 59 · 2020: 96 · 2019: 104 · 2018: 88 · 2017: 83 · 2016: 64 · 2015: 79 · 2014: 86 · 2013: 97 · 2012: 81
FWCI
64.91
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review Letters (publishedVersion)
  • PubMed (publishedVersion)
Topics
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Cellular Automata and Applications
  • Physical Sciences › Engineering › Computational Mechanics › Lattice Boltzmann Simulation Studies
  • Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › Computer Graphics and Visualization Techniques
Keywords
lattice gas automata, Navier-Stokes equations, massively parallel computing, fluid dynamics simulation, cellular automata

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review