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Stable multispeed lattice Boltzmann methods

R. A. Brownlee·A. N. Gorban·J. Levesley
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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.

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R. A. Brownlee, A. N. Gorban, J. Levesley. 2006-12-07. Stable multispeed lattice Boltzmann methods. https://arxiv.org/abs/cond-mat/0611616

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