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On Triangular Lattice Boltzmann Schemes for Scalar Problems

Published online by Cambridge University Press:  03 June 2015

François Dubois  and
Pierre Lallemand
François Dubois*
Affiliation:
Conservatoire National des Arts et Métiers, Department of Mathematics, Paris, and Department of Mathematics, University Paris-Sud, Bât. 425, F-91405 Orsay Cedex, France
Pierre Lallemand
Affiliation:
Centre National de la Recherche Scientifique, Paris, France
*
Corresponding author.Email:francois.dubois@math.u-psud.fr
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Abstract

We propose to extend the d’Humieres version of the lattice Boltzmann scheme to triangular meshes. We use Bravais lattices or more general lattices with the property that the degree of each internal vertex is supposed to be constant. On such meshes, it is possible to define the lattice Boltzmann scheme as a discrete particle method, without need of finite volume formulation or Delaunay-Voronoi hypothesis for the lattice. We test this idea for the heat equation and perform an asymptotic analysis with the Taylor expansion method for two schemes named D2T4 and D2T7. The results show a convergence up to second order accuracy and set new questions concerning a possible super-convergence.

Keywords

65-0565Q9982C20Laplacian operatorheat equationd’Humieres schemeD2T4D2T7

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Type
Research Article
Information
Communications in Computational Physics , Volume 13 , Issue 3 , March 2013 , pp. 649 - 670
Copyright
Copyright © Global Science Press Limited 2013

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