Momentum transfer of a Boltzmann-lattice fluid with boundaries
Abstract
We study the velocity boundary condition for curved boundaries in the lattice Boltzmann equation (LBE). We propose a LBE boundary condition for moving boundaries by combination of the “bounce-back” scheme and spatial interpolations of first or second order. The proposed boundary condition is a simple, robust, efficient, and accurate scheme. Second-order accuracy of the boundary condition is demonstrated for two cases: (1) time-dependent two-dimensional circular Couette flow and (2) two-dimensional steady flow past a periodic array of circular cylinders (flow through the porous media of cylinders). For the former case, the lattice Boltzmann solution is compared with the analytic solution of the Navier–Stokes equation. For the latter case, the lattice Boltzmann solution is compared with a finite-element solution of the Navier–Stokes equation. The lattice Boltzmann solutions for both flows agree very well with the solutions of the Navier–Stokes equations. We also analyze the torque due to the momentum transfer between the fluid and the boundary for two initial conditions: (a) impulsively started cylinder and the fluid at rest, and (b) uniformly rotating fluid and the cylinder at rest.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The interpolated boundary method offers robustness in terms of stability for the staircase approximation of the sponge structure.
“The interpolated boundary method offers robustness in terms of stability for the staircase approximation of the sponge structure.”
From Comprehensive Computational Model for Coupled Fluid Flow, Mass Transfer, and Light Supply in Tubular Photobioreactors Equipped with Glass Sponges (2022) · cites this paper as [54]
Cites
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
Saad, Y., & Schultz, M. H. (1986) · SIAM Journal on Scientific and Statistical Computing · doi:10.1137/0907058 · Cited by 11,280 · see citing works
LATTICE BOLTZMANN METHOD FOR FLUID FLOWS
Chen, S., & Doolen, G. D. (1998) · Annual Review of Fluid Mechanics · doi:10.1146/annurev.fluid.30.1.329 · Cited by 7,336 · see citing works
Lattice BGK Models for Navier-Stokes Equation
Qian, Y., d’Humières, D., & Lallemand, P. (1992) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/17/6/001 · Cited by 5,326 · see citing works
Self-citationLattice-gas automata for the Navier-Stokes equation
Frisch, U., Hasslacher, B., & Pomeau, Y. (1986) · Physical Review Letters · doi:10.1103/physrevlett.56.1505 · Cited by 2,788 · see citing works
Lallemand, P., & Luo, L. (2000) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.61.6546 · Cited by 2,292 · see citing works
Self-citationUse of the Boltzmann Equation to Simulate Lattice-Gas Automata
McNamara, G. R., & Zanetti, G. (1988) · Physical Review Letters · doi:10.1103/physrevlett.61.2332 · Cited by 2,096 · see citing works
The lattice Boltzmann equation: theory and applications
Benzi, R., Succi, S., & Vergassola, M. (1992) · Physics Reports · doi:10.1016/0370-1573(92)90090-m · Cited by 2,089 · see citing works
Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method
Chen, H., Chen, S., & Matthaeus, W. H. (1992) · Physical Review A · doi:10.1103/physreva.45.r5339 · Cited by 1,562 · see citing works
Lattice Boltzmann Model for the Incompressible Navier–Stokes Equation
He, X., & Luo, L. (1997) · Journal of Statistical Physics · doi:10.1023/b:joss.0000015179.12689.e4 · Cited by 1,256 · see citing works
Lattice Gas Dynamics with Enhanced Collisions
Higuera, F. J., Succi, S., & Benzi, R. (1989) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/9/4/008 · Cited by 934 · see citing works
Lattice gas hydrodynamics in two and three dimensions
Frisch, U., d’Humières, D., Hasslacher, B., et al. (1986) · University of North Texas Digital Library (University of North Texas) · Cited by 903 · see citing works
Boltzmann Approach to Lattice Gas Simulations
Higuera, F. J., & Jiménez, J. L. (1989) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/9/7/009 · Cited by 881 · see citing works
He, X., Zou, Q., Luo, L., et al. (1997) · Journal of Statistical Physics · doi:10.1007/bf02181482 · Cited by 729 · see citing works
Grid Refinement for Lattice-BGK Models
Filippova, O., & Hänel, D. (1998) · Journal of Computational Physics · doi:10.1006/jcph.1998.6089 · Cited by 690 · see citing works
Slow flow past periodic arrays of cylinders with application to heat transfer
Sangani, A. S., & Acrivos, A. (1982) · International Journal of Multiphase Flow · doi:10.1016/0301-9322(82)90029-5 · Cited by 632 · see citing works
An Accurate Curved Boundary Treatment in the Lattice Boltzmann Method
Mei, R., Luo, L., & Shyy, W. (1999) · Journal of Computational Physics · doi:10.1006/jcph.1999.6334 · Cited by 596 · see citing works
On boundary conditions in lattice Boltzmann methods
Chen, S., Martínez, D. O., & Mei, R. (1996) · Physics of Fluids · doi:10.1063/1.869035 · Cited by 500 · see citing works
Boundary conditions for lattice Boltzmann simulations
Ziegler, D. P. (1993) · Journal of Statistical Physics · doi:10.1007/bf01049965 · Cited by 435 · see citing works
Initial and boundary conditions for the lattice Boltzmann method
Skordos, P. A. (1993) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.48.4823 · Cited by 428 · see citing works
Boundary flow condition analysis for the three-dimensional lattice Boltzmann model
Ginzbourg, I., & Adler, P. M. (1994) · Journal de Physique II · doi:10.1051/jp2:1994123 · Cited by 397 · see citing works
A consistent hydrodynamic boundary condition for the lattice Boltzmann method
Noble, D. R., Chen, S., Georgiadis, J. G., et al. (1995) · Physics of Fluids · doi:10.1063/1.868767 · Cited by 361 · see citing works
A non-slip boundary condition for lattice Boltzmann simulations
Inamuro, T., Yoshino, M., & Ogino, F. (1995) · Physics of Fluids · doi:10.1063/1.868766 · Cited by 327 · see citing works
Rarefied Gas Dynamics: Theory and Simulations
(1994) · American Institute of Aeronautics and Astronautics eBooks · doi:10.2514/4.866319 · Cited by 298 · see citing works
Moderate Reynolds number flows through periodic and random arrays of aligned cylinders
Koch, D. L., & Ladd, A. J. C. (1997) · Journal of Fluid Mechanics · doi:10.1017/s002211209700671x · Cited by 278 · see citing works
Nonlinear corrections to Darcy's law at low Reynolds numbers
Firdaouss, M., Guermond, J., & Quéré, P. L. (1997) · Journal of Fluid Mechanics · doi:10.1017/s0022112097005843 · Cited by 219 · see citing works
Self-citationA Knudsen layer theory for lattice gases
Cornubert, R., d’Humières, D., & Levermore, D. (1991) · Physica D Nonlinear Phenomena · doi:10.1016/0167-2789(91)90295-k · Cited by 210 · see citing works
Local second-order boundary methods for lattice Boltzmann models
Ginzbourg, I., & d’Humières, D. (1996) · Journal of Statistical Physics · doi:10.1007/bf02174124 · Cited by 173 · see citing works
Solid-fluid boundaries in particle suspension simulations via the lattice Boltzmann method
Behrend, O. (1995) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.52.1164 · Cited by 82 · see citing works
Analytic Solutions of Linearized Lattice Boltzmann Equation for Simple Flows
Luo, L. (1997) · Journal of Statistical Physics · doi:10.1023/b:joss.0000015178.19008.78 · Cited by 54 · see citing works
Lattice Boltzmann Method for Irregular Grids
Karlin, I. V., Succi, S., & Orszag, S. A. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.5245 · Cited by 31 · see citing works
Some remarks on the acoustic parameters of sharp-edged porous media
Firdaouss, M., Guermond, J., & Lafarge, D. (1998) · International Journal of Engineering Science · doi:10.1016/s0020-7225(98)00002-0 · Cited by 18 · see citing works
Self-citation
Flagged first, then by citations
Cited by
Sorted by citations
Lattice-Boltzmann method for complex flows
Aidun, C. K., & Clausen, J. R. (2010) · Annual Review of Fluid Mechanics · doi:10.1146/annurev-fluid-121108-145519 · Cited by 1,991 · see citing works
OpenLB—Open source lattice Boltzmann code
Krause, M. J., Kummerländer, A., Avis, S. J., Kusumaatmaja, H., Dapelo, D., Klemens, F., Gaedtke, M., Hafen, N., Mink, A., Trunk, R., et al. (2021) · Computers & Mathematics with Applications · doi:10.1016/j.camwa.2020.04.033 · Cited by 203 · see citing works
Mink, A., Schediwy, K., Posten, C., Nirschl, H., Simonis, S., & Krause, M. J. (2022) · Energies · doi:10.3390/en15207671 · Cited by 30 · see citing works
Gaedtke, M., Hoffmann, T., Reinhardt, V., Thäter, G., Nirschl, H., & Krause, M. J. (2019) · International Journal of Modern Physics C · doi:10.1142/s012918311950013x · Cited by 12 · see citing works
Nathen, P., Gaudlitz, D., Krause, M., & Kratzke, J. (2013) · 21st AIAA Computational Fluid Dynamics Conference · doi:10.2514/6.2013-2573 · Cited by 9 · see citing works
Fluid–Structure Interaction Simulation of a Coriolis Mass Flowmeter Using a Lattice Boltzmann Method
Haussmann, M., Reinshaus, P., Simonis, S., Nirschl, H., & Krause, M. J. (2021) · Fluids · doi:10.3390/fluids6040167 · Cited by 1 · see citing works
- Authors
- Bouzidi, M., Firdaouss, M., & Lallemand, P.
- Affiliations
- Université Paris-Sud (FR)
- Venue
- Physics of Fluids
- Publisher
- AIP Publishing
- Published
- 2001-11-01
- Volume
- 13
- Issue
- 11
- Pages
- 3452-3459
- ISSN
- 1070-6631 (ISSN-L)
- 1089-7666
- OpenAlex
- W2095470085
- Cited by
- 1,251
- References
- 31
- Citations by year
- 2026: 71 · 2025: 85 · 2024: 56 · 2023: 81 · 2022: 86 · 2021: 93 · 2020: 59 · 2019: 73 · 2018: 67 · 2017: 61 · 2016: 62 · 2015: 54 · 2014: 40 · 2013: 46 · 2012: 44
- FWCI
- 12.03
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physics of Fluids (publishedVersion)
- Topics
- Physical Sciences › Engineering › Computational Mechanics › Lattice Boltzmann Simulation Studies
- Physical Sciences › Mathematics › Applied Mathematics › Gas Dynamics and Kinetic Theory
- Physical Sciences › Engineering › Computational Mechanics › Computational Fluid Dynamics and Aerodynamics
- Keywords
- lattice Boltzmann equation, curved boundaries, moving boundary, spatial interpolation, velocity boundary conditions, momentum transfer, circular Couette flow, cylinder flow, porous media, torque, Navier-Stokes equations
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
