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Title: Stable multispeed lattice Boltzmann methods
Authors: Brownlee, R.A.
Gorban, Alexander N.
Levesley, Jeremy
First Published: 2006
Publisher: Dept. of Mathematics, University of Leicester
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.
Series/Report no.: MA 06-026
Type: Report
Appears in Collections:Reports, Dept. of Mathematics

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