Colloquium: Role of the H theorem in lattice Boltzmann hydrodynamic simulations
Colloquium: Role of the H theorem in lattice Boltzmann hydrodynamic simulations
In the last decade, minimal kinetic models, and primarily the lattice Boltzmann equation, have met with significant success in the simulation of complex hydrodynamic phenomena, ranging from slow flows in grossly irregular geometries to fully developed turbulence, to flows with dynamic phase transitions. Besides their practical value as efficient computational tools for the dynamics of complex systems, these minimal models may also represent a new conceptual paradigm in modern computational statistical mechanics: instead of proceeding bottom-up from the underlying microdynamic systems, these minimal kinetic models are built top-down starting from the macroscopic target equations. This procedure can provide dramatic advantages, provided the essential physics is not lost along the way. For dissipative systems, one essential requirement is compliance with the second law of thermodynamics. In this Colloquium, the authors present a chronological survey of the main ideas behind the lattice Boltzmann method, with special focus on the role played by the H theorem in enforcing compliance of the method with macroscopic evolutionary constraints (the second law) as well as in serving as a numerically stable computational tool for fluid flows and other dissipative systems out of equilibrium.
1203-1220
Succi, S.
159d4d9f-4607-4485-8fca-4d7ad11db6f4
Karlin, I.V.
3f0e01a2-c4d9-4210-9ef3-47e6c426cc8a
Chen, H.
d30e2017-5be4-4a58-aacd-13fec55ae5f2
October 2002
Succi, S.
159d4d9f-4607-4485-8fca-4d7ad11db6f4
Karlin, I.V.
3f0e01a2-c4d9-4210-9ef3-47e6c426cc8a
Chen, H.
d30e2017-5be4-4a58-aacd-13fec55ae5f2
Succi, S., Karlin, I.V. and Chen, H.
(2002)
Colloquium: Role of the H theorem in lattice Boltzmann hydrodynamic simulations.
Reviews of Modern Physics, 74 (4), .
(doi:10.1103/RevModPhys.74.1203).
Abstract
In the last decade, minimal kinetic models, and primarily the lattice Boltzmann equation, have met with significant success in the simulation of complex hydrodynamic phenomena, ranging from slow flows in grossly irregular geometries to fully developed turbulence, to flows with dynamic phase transitions. Besides their practical value as efficient computational tools for the dynamics of complex systems, these minimal models may also represent a new conceptual paradigm in modern computational statistical mechanics: instead of proceeding bottom-up from the underlying microdynamic systems, these minimal kinetic models are built top-down starting from the macroscopic target equations. This procedure can provide dramatic advantages, provided the essential physics is not lost along the way. For dissipative systems, one essential requirement is compliance with the second law of thermodynamics. In this Colloquium, the authors present a chronological survey of the main ideas behind the lattice Boltzmann method, with special focus on the role played by the H theorem in enforcing compliance of the method with macroscopic evolutionary constraints (the second law) as well as in serving as a numerically stable computational tool for fluid flows and other dissipative systems out of equilibrium.
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Published date: October 2002
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Local EPrints ID: 49171
URI: http://eprints.soton.ac.uk/id/eprint/49171
ISSN: 0034-6861
PURE UUID: d3c859b9-8d66-4a11-a902-cabb592b545b
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Date deposited: 24 Oct 2007
Last modified: 15 Mar 2024 09:53
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Author:
S. Succi
Author:
I.V. Karlin
Author:
H. Chen
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