Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
Cited by 1,744

The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.

Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation

He, Xiaoyi, Luo, Li-Shi·1997·Physical Review E
DOI 10.1103/physreve.56.6811
Open this paper in CoChat — free account

Abstract

In this paper, the lattice Boltzmann equation is directly derived from the Boltzmann equation. It is shown that the lattice Boltzmann equation is a special discretized form of the Boltzmann equation. Various approximations for the discretization of the Boltzmann equation in both time and phase space are discussed in detail. A general procedure to derive the lattice Boltzmann model from the continuous Boltzmann equation is demonstrated explicitly. The lattice Boltzmann models derived include the two-dimensional 6-bit, 7-bit, and 9-bit, and three-dimensional 27-bit models.

Overview

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/physreve.56.6811

Cites

1 of 1 references verified0 citation errors · 0 not checkable

Statistics

Verification

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.

Citations

Cites

Show all 1 references

Research works printed but not linked: 38

  1. G. McNamara, 1988, Phys. Rev. Lett., 61, 2332, 10.1103/PhysRevLett.61.2332 · DOI · Paper page
  2. F. J. Higuera, 1989, Europhys. Lett., 9, 345, 10.1209/0295-5075/9/4/008 · DOI
  3. H. Chen, 1991, Phys. Rev. A, 45, R5339, 10.1103/PhysRevA.45.R5339 · DOI
  4. Y. H. Qian, 1992, Europhys. Lett., 17, 479, 10.1209/0295-5075/17/6/001 · DOI
  5. 1990, Lattice Gas Methods for Partial Differential Equations
  6. 1991, Lattice Gas Methods: Theory, Applications, and Hardware
  7. R. Benzi, 1992, Phys. Rep., 222, 145, 10.1016/0370-1573(92)90090-M · DOI · Paper page
  8. S. Chen, 1991, Phys. Rev. Lett., 67, 3776, 10.1103/PhysRevLett.67.3776 · DOI · Paper page
  9. X. Shan, 1993, Phys. Rev. E, 47, 1815, 10.1103/PhysRevE.47.1815 · DOI
  10. M. R. Swift, 1995, Phys. Rev. Lett., 75, 830, 10.1103/PhysRevLett.75.830 · DOI · Paper page
  11. A. J. C. Ladd, 1994, J. Fluid Mech., 271, 285, 10.1017/S0022112094001771 · DOI
  12. B. M. Boghosian, 1996, Proc. R. Soc. Ser. A, 452, 1221, 10.1098/rspa.1996.0063 · DOI
  13. S. Chen, 1995, Comput. Chem. Eng., 19, 617, 10.1016/0098-1354(94)00072-7 · DOI
  14. S. Chen, 1991, Physica D, 47, 72, 10.1016/0167-2789(91)90281-D · DOI
  15. S. Wolfram, 1986, J. Stat. Phys., 45, 471, 10.1007/BF01021083 · DOI · Paper page
  16. U. Frisch, 1987, Complex Syst., 1, 649
  17. P. L. Bhatnagar, 1954, Phys. Rev., 94, 511, 10.1103/PhysRev.94.511 · DOI · Paper page
  18. S. Harris, 1971, An Introduction to the Theory of the Boltzmann Equation
  19. R. L. Liboff, 1990, Kinetic Theory
  20. J. M. V. A. Koelman, 1991, Europhys. Lett., 15, 603, 10.1209/0295-5075/15/6/007 · DOI
  21. G. McNamara, 1993, Physica A, 194, 218, 10.1016/0378-4371(93)90356-9 · DOI
  22. F. J. Alexander, 1993, Phys. Rev. E, 47, R2249, 10.1103/PhysRevE.47.R2249 · DOI · Paper page
  23. Y. Chen, 1994, Phys. Rev. E, 50, 2766, 10.1103/PhysRevB.50.2766 · DOI
  24. G. McNamara, 1995, J. Stat. Phys., 81, 395, 10.1007/BF02179986 · DOI · Paper page
  25. S. Succi, 1995, J. Stat. Phys., 81, 5, 10.1007/BF02179964 · DOI
  26. X. He, 1997, Phys. Rev. E, 55, R6333, 10.1103/PhysRevE.55.R6333 · DOI · Paper page
  27. X. He, 1996, J. Comput. Phys., 129, 357, 10.1006/jcph.1996.0255 · DOI · Paper page
  28. X. He, 1997, Physica A, 239, 276, 10.1016/S0378-4371(96)00486-4 · DOI
  29. K. H. Prendergast, 1993, J. Comput. Phys., 109, 53, 10.1006/jcph.1993.1198 · DOI
  30. K. Xu, 1993, J. Comput. Phys., 114, 9, 10.1006/jcph.1994.1145 · DOI
  31. K. Xu, 1995, J. Comput. Phys., 120, 48, 10.1006/jcph.1995.1148 · DOI
  32. K. Xu, 1995, J. Stat. Phys., 81, 147, 10.1007/BF02179973 · DOI
  33. K. Xu, 1996, Int. J. Comput. Fluid Dyn., 7, 213, 10.1080/10618569608940763 · DOI
  34. K. Xu, 1997, J. Comput. Phys., 134, 122, 10.1006/jcph.1997.5677 · DOI
  35. A. D. Kotelnikov, 1997, J. Comput. Phys., 134, 364, 10.1006/jcph.1997.5720 · DOI
  36. C. D. Levermore, 1996, J. Stat. Phys., 83, 1021, 10.1007/BF02179552 · DOI
  37. P. J. Davis, 1984, Methods of Numerical Integration, 2nd ed.
  38. N. M. Steen, 1969, Math. Comput., 23, 661

Cited by

See all 1,744

Metadata

Authors
He, X., & Luo, L.-S.
Venue
Physical Review E
Publisher
American Physical Society (APS)
Published
1997-12-01
Volume
56
Issue
6
Pages
6811-6817
ISSN
  • 1063-651X (ISSN-L)
  • 1095-3787
DOI
10.1103/physreve.56.6811
OpenAlex
W2062900651
Cited by
1,744
References
1
FWCI
11.17
Type
journal article
Language
en
Open access
closed
Licence
link.aps.org/licenses/aps-default-license (vor)

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

How to cite

Cite CoChat for the checks on this page, and the paper for its own findings.

This page
CoChat. (2026). Citation check: Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation. https://app.cochat.ai/papers/10.1103/physreve.56.6811
The paper
He, X., & Luo, L.-S. (1997). Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation. Physical Review E. https://doi.org/10.1103/physreve.56.6811

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.