Colloquium: Role of the H theorem in lattice Boltzmann hydrodynamic simulations
By Sauro Succi, I. Karlin, Hudong Chen. 2002
168 citations recorded by the source corpus.
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.
Subfields: Computational Mechanics
View Paper: https://www.semanticscholar.org/paper/6bb2ce98ca3365802f1eba6e69ecacb8d335faa3
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In Computational Mechanics
- Dominique d'Humières
- Frederik Verhaeghe
- Irina Ginzburg
- Alexander N Gorban
- Paul J. Dellar
- I. Karlin
- A. Zinovyev
- Li-Shi Luo
Citations in the corpus
- Incompressible limits of lattice Boltzmann equations using multiple relaxation times (2003, methodology): “In particular, the right hand side of (5) should conserve mass and momentum, in the sense that [4, 33]”
- Constructive methods of invariant manifolds for kinetic problems (2003, methodology): “The proof of the H theorem in the framework of the Lattice Boltzmann method has been only very recently achieved [92].”
- Study of Simple Hydrodynamic Solutions with the Two-Relaxation-Times Lattice Boltzmann Scheme (2008, background): “The reader can also find in [37] an exhaustive review on the possibility to increase the stability of the BGK model at low viscosity with the help of an alternative, entropy based, equilibrium.”