Stabilisation of the lattice-Boltzmann method using the Ehrenfests' coarse-graining

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dc.creatorBrownlee, R. A.
dc.creatorGorban, A. N.
dc.creatorLevesley, J.
dc.date2006-05-15
dc.date2006-05-23
dc.date.accessioned2026-07-07T07:08:56Z
dc.date.available2026-07-07T07:08:56Z
dc.descriptionThe lattice-Boltzmann method (LBM) and its variants have emerged as promising, computationally efficient and increasingly popular numerical methods for modelling complex fluid flow. However, it is acknowledged that the method can demonstrate numerical instabilities, e.g., in the vicinity of shocks. We propose a simple and novel technique to stabilise the lattice-Boltzmann method by monitoring the difference between microscopic and macroscopic entropy. Populations are returned to their equilibrium states if a threshold value is exceeded. We coin the name Ehrenfests' steps for this procedure in homage to the vehicle that we use to introduce the procedure, namely, the Ehrenfests' idea of coarse-graining. The one-dimensional shock tube for a compressible isothermal fluid is a standard benchmark test for hydrodynamic codes. We observe that, of all the LBMs considered in the numerical experiment with the one-dimensional shock tube, only the method which includes Ehrenfests' steps is capable of suppressing spurious post-shock oscillations.
dc.description4 pages, 9 figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0605359
dc.identifierhttp://arxiv.org/abs/cond-mat/0605359
dc.identifierPhys Rev E 74 (2006), 037703
dc.identifierdoi:10.1103/PhysRevE.74.037703
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/110889
dc.subjectStatistical Mechanics
dc.subjectMaterials Science
dc.titleStabilisation of the lattice-Boltzmann method using the Ehrenfests' coarse-graining
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