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Stable multispeed lattice Boltzmann methods

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

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. \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
OAI identifier: oai:lra.le.ac.uk:2381/4278

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Citations

  1. (2006). Gorban, in Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena (Springer, doi
  2. (2005). Invariant manifolds for physical and chemical kinetics, vol. 660 of Lect. Notes Phys. doi
  3. (2001). The lattice Boltzmann equation for fluid dynamics and beyond (OUP, doi
  4. This work is supported by Engineering and Physical Sciences Research Council (EPSRC) grant number GR/S95572/01.

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