Commun. Comput. Phys., 13 (2013), pp. 649-670.


On Triangular Lattice Boltzmann Schemes for Scalar Problems

Francois Dubois 1*, Pierre Lallemand 2

1 Conservatoire National des Arts et Metiers, Department of Mathematics, Paris, and Department of Mathematics, University Paris-Sud, Bat. 425, F-91405 Orsay Cedex, France.
2 Centre National de la Recherche Scientifique, Paris, France.

Received 31 October 2011; Accepted (in revised version) 27 January 2012
Available online 29 August 2012
doi:10.4208/cicp.381011.270112s

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.

AMS subject classifications: 65-05, 65Q99, 82C20

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Key words: Laplacian operator, heat equation, d'Humieres scheme, D2T4, D2T7.

*Corresponding author.
Email: francois.dubois@math.u-psud.fr (F. Dubois)
 

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