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Stable multispeed lattice Boltzmann methods

By R.A. Brownlee, Alexander N. Gorban and Jeremy Levesley


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. \ud 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. \ud The equations are true

Publisher: Dept. of Mathematics, University of Leicester
Year: 2006
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  4. This work is supported by Engineering and Physical Sciences Research Council (EPSRC) grant number GR/S95572/01.

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