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Elements of the lattice Boltzmann method I: linear advection equation

Elements of the lattice Boltzmann method I: linear advection equation
Elements of the lattice Boltzmann method I: linear advection equation
This paper opens a series of papers aimed at finalizing the development of the lattice Boltzmann method for complex hydrodynamic systems. The lattice Boltzmann method is introduced at the elementary level of the linear advection equation. Details are provided on lifting the target macroscopic equations to a kinetic equation, and, after that, to the fully discrete lattice Boltzmann scheme. The over-relaxation method is put forward as a cornerstone of the second-order temporal discretization, and its enhancement with the use of the entropy estimate is explained in detail. A new asymptotic expansion of the entropy estimate is derived, and implemented in the sample code. It is shown that the lattice Boltzmann method provides a computationally efficient way of numerically solving the advection equation with a controlled amount of numerical dissipation, while retaining positivity.
lattice boltzmann method, implicit schemes, advection, entropy, invariant manifold, kinetic theory
1815-2406
616-655
Karlin, I.V.
3f0e01a2-c4d9-4210-9ef3-47e6c426cc8a
Ansumali, S.
419cb861-d1f8-4532-a1ab-2b56135391b5
Frouzakis, C.E.
69f46c40-d7f7-41f3-a166-c0311158b821
Chikatamarla, S.S.
edd9c515-cfeb-436c-a562-61171f2e0290
Karlin, I.V.
3f0e01a2-c4d9-4210-9ef3-47e6c426cc8a
Ansumali, S.
419cb861-d1f8-4532-a1ab-2b56135391b5
Frouzakis, C.E.
69f46c40-d7f7-41f3-a166-c0311158b821
Chikatamarla, S.S.
edd9c515-cfeb-436c-a562-61171f2e0290

Karlin, I.V., Ansumali, S., Frouzakis, C.E. and Chikatamarla, S.S. (2006) Elements of the lattice Boltzmann method I: linear advection equation. Communications in Computational Physics, 1 (4), 616-655.

Record type: Article

Abstract

This paper opens a series of papers aimed at finalizing the development of the lattice Boltzmann method for complex hydrodynamic systems. The lattice Boltzmann method is introduced at the elementary level of the linear advection equation. Details are provided on lifting the target macroscopic equations to a kinetic equation, and, after that, to the fully discrete lattice Boltzmann scheme. The over-relaxation method is put forward as a cornerstone of the second-order temporal discretization, and its enhancement with the use of the entropy estimate is explained in detail. A new asymptotic expansion of the entropy estimate is derived, and implemented in the sample code. It is shown that the lattice Boltzmann method provides a computationally efficient way of numerically solving the advection equation with a controlled amount of numerical dissipation, while retaining positivity.

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More information

Published date: August 2006
Keywords: lattice boltzmann method, implicit schemes, advection, entropy, invariant manifold, kinetic theory

Identifiers

Local EPrints ID: 49251
URI: http://eprints.soton.ac.uk/id/eprint/49251
ISSN: 1815-2406
PURE UUID: f6235c8a-f03f-4ca0-9323-1cfbe1c3bfc1

Catalogue record

Date deposited: 26 Oct 2007
Last modified: 11 Dec 2021 16:53

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Contributors

Author: I.V. Karlin
Author: S. Ansumali
Author: C.E. Frouzakis
Author: S.S. Chikatamarla

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