Stable multispeed lattice Boltzmann methods
Abstract
We demonstrate how to produce a stable multispeed lattice Boltzmann method (LBM) for a wide range of velocity sets, many of which were previously thought to be intrinsically unstable. We use non-Gauss--Hermitian cubatures. The method operates stably for almost zero viscosity, has second-order accuracy, suppresses typical spurious oscillation (only a modest Gibbs effect is present) and introduces no artificial viscosity. There is almost no computational cost for this innovation. DISCLAIMER: Additional tests and wide discussion of this preprint show that the claimed property of coupled steps: no artificial dissipation and the second-order accuracy of the method are valid only on sufficiently fine grids. For coarse grids the higher-order terms destroy coupling of steps and additional dissipation appears. The equations are true.
Cite
@article{arxiv.cond-mat/0611616,
title = {Stable multispeed lattice Boltzmann methods},
author = {R. A. Brownlee and A. N. Gorban and J. Levesley},
journal= {arXiv preprint arXiv:cond-mat/0611616},
year = {2007}
}
Comments
Disclaimer about the area of applicability is added to abstract