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Title: Stabilisation of the lattice-Boltzmann method using the Ehrenfests' coarse-graining
Authors: Brownlee, R.A.
Gorban, Alexander N.
Levesley, Jeremy
First Published: 2006
Publisher: Dept. of Mathematics, University of Leicester
Abstract: The lattice-Boltzmann method (LBM) and its variants have emerged as promising, computationally efficient and increasingly popular numerical methods for modelling complex fuid 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.
Series/Report no.: MA 06-008
Type: Report
Appears in Collections:Reports, Dept. of Mathematics

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