Entropic Lattice Boltzmann Model for Burgers's Equation

Entropic lattice Boltzmann models are discrete-velocity models of hydrodynamics that possess a Lyapunov function. This feature makes them useful as nonlinearly stable numerical methods for integrating hydrodynamic equations. Over the last few years, such models have been successfully developed for t...

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Veröffentlicht in:	Philosophical Transactions: Mathematical, Physical and Engineering Sciences. - The Royal Society. - 362(2004), 1821, Seite 1691-1701
1. Verfasser:	Boghosian, Bruce M. (VerfasserIn)
Weitere Verfasser:	Yepez, Jeffrey
Format:	Online-Aufsatz
Sprache:	English
Veröffentlicht:	2004
Zugriff auf das übergeordnete Werk:	Philosophical Transactions: Mathematical, Physical and Engineering Sciences
Schlagworte:	Lattice Boltzmann Burgers's Equation Kinetic Theory Physical sciences Mathematics Philosophy Applied sciences


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520			\|a Entropic lattice Boltzmann models are discrete-velocity models of hydrodynamics that possess a Lyapunov function. This feature makes them useful as nonlinearly stable numerical methods for integrating hydrodynamic equations. Over the last few years, such models have been successfully developed for the Navier-Stokes equations in two and three dimensions, and have been proposed as a new category of subgrid model of turbulence. In the present work we develop an entropie lattice Boltzmann model for Burgers's equation in one spatial dimension. In addition to its pedagogical value as a simple example of such a model, our result is actually a very effective way to simulate Burgers's equation in one dimension. At moderate to high values of viscosity, we confirm that it exhibits no trace of instability. At very small values of viscosity, however, we report the existence of oscillations of bounded amplitude in the vicinity of the shock, where gradient scale lengths become comparable with the grid size. As the viscosity decreases, the amplitude at which these oscillations saturate tends to increase. This indicates that, in spite of their nonlinear stability, entropie lattice Boltzmann models may become inaccurate when the ratio of gradient scale length to grid spacing becomes too small. Similar inaccuracies may limit the utility of the entropie lattice Boltzmann paradigm as a subgrid model of Navier-Stokes turbulence.
540			\|a Copyright 2004 The Royal Society
650		4	\|a Lattice Boltzmann
650		4	\|a Burgers's Equation
650		4	\|a Kinetic Theory
650		4	\|a Physical sciences \|x Physics \|x Mechanics \|x Fluid mechanics \|x Viscosity
650		4	\|a Physical sciences \|x Physics \|x Mechanics \|x Fluid mechanics \|x Fluid dynamics \|x Turbulence \|x Turbulence models
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Descriptive statistics \|x Statistical distributions \|x Distribution functions
650		4	\|a Philosophy \|x Logic \|x Logical topics \|x Formal logic \|x Mathematical logic \|x Mathematical set theory \|x Lattice theory \|x Mathematical lattices
650		4	\|a Applied sciences \|x Research methods \|x Modeling
650		4	\|a Mathematics \|x Mathematical expressions \|x Mathematical functions \|x Scalar functions \|x Liapunov functions
650		4	\|a Physical sciences \|x Physics \|x Mechanics \|x Fluid mechanics \|x Fluid dynamics \|x Turbulence
650		4	\|a Physical sciences \|x Physics \|x Mechanics \|x Classical mechanics \|x Kinematics \|x Equations of motion \|x Kinetic equations \|x Hydrodynamic equations
650		4	\|a Mathematics \|x Mathematical analysis \|x Mathematical models
650		4	\|a Physical sciences \|x Physics \|x Mechanics \|x Fluid mechanics \|x Fluid dynamics \|x Hydrodynamics
655		4	\|a research-article
700	1		\|a Yepez, Jeffrey \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Philosophical Transactions: Mathematical, Physical and Engineering Sciences \|d The Royal Society \|g 362(2004), 1821, Seite 1691-1701 \|w (DE-627)254635296 \|w (DE-600)1462626-3 \|x 1364503X \|7 nnns
773	1	8	\|g volume:362 \|g year:2004 \|g number:1821 \|g pages:1691-1701
856	4	0	\|u https://www.jstor.org/stable/4142373 \|3 Volltext
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