The DOI matches its Crossref record; 23 of the 23 references it cites were found in a registry or an index.
Extended Boltzmann Kinetic Equation for Turbulent Flows
Abstract
Complex fluid physics can be modeled using an extended kinetic (Boltzmann) equation in a more efficient way than using the continuum Navier-Stokes equations. Here, we explain this method for modeling fluid turbulence and show its effectiveness with the use of a computationally efficient implementation in terms of a discrete or “lattice” Boltzmann equation.
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Cites
The numerical computation of turbulent flows
Launder, B. E., & Spalding, D. B. (1974) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(74)90029-2 · Cited by 12,833
Bhatnagar, P. L., Gross, E. P., & Krook, M. (1954) · Physical Review · doi:10.1103/physrev.94.511 · Cited by 8,543
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 7,314
Lattice BGK Models for Navier-Stokes Equation
Qian, Y. H., D'Humières, D., & Lallemand, P. (1992) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/17/6/001 · Cited by 5,303
Turbulence: The Legacy of A.N. Kolmogorov
Frisch, U. (1995) · Cambridge University Press eBooks · doi:10.1017/cbo9781139170666 · Cited by 5,045
Renormalization group analysis of turbulence. I. Basic theory
Yakhot, V., & Orszag, S. A. (1986) · Journal of Scientific Computing · doi:10.1007/bf01061452 · Cited by 4,265
Self-citationThe Lattice Boltzmann Equation for Fluid Dynamics and Beyond
Succi, S. (2001) · doi:10.1093/oso/9780198503989.001.0001 · Cited by 4,188
Self-citationDevelopment of turbulence models for shear flows by a double expansion technique
Yakhot, V., Orszag, S. A., Thangam, S., Gatski, T. B., & Speziale, C. G. (1992) · Physics of Fluids A: Fluid Dynamics · doi:10.1063/1.858424 · Cited by 2,832
Self-citationThe Lattice Boltzmann Equation: For Fluid Dynamics and Beyond
Yeomans, J. M. (2001) · Cited by 2,741
Use 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 2,079
Cited by
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
Nathen, P., Gaudlitz, D., Krause, M., & Kratzke, J. (2013) · 21st AIAA Computational Fluid Dynamics Conference · doi:10.2514/6.2013-2573 · Cited by 9
Metadata
- Authors
- Chen, H., Kandasamy, S., Orszag, S., Shock, R., Succi, S., & Yakhot, V.
- Venue
- Science
- Published
- 2003-08
- Volume
- 301
- Issue
- 5633
- Pages
- 633-636
- ISSN
- 0036-8075 (ISSN-L)
- 1095-9203
- OpenAlex
- W2019645917
- Cited by
- 720
- References
- 23
- FWCI
- 27.30
- Type
- journal article
- Language
- en
- Open access
- closed
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- Chen, H., Kandasamy, S., Orszag, S., Shock, R., Succi, S., & Yakhot, V. (2003). Extended Boltzmann Kinetic Equation for Turbulent Flows. Science. https://doi.org/10.1126/science.1085048
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