Volume 13, Issue 3
On Triangular Lattice Boltzmann Schemes for Scalar Problems

François Dubois and Pierre Lallemand


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

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  • Abstract

We propose to extend the d’Humie`res version of the lattice Boltzmann scheme totriangular meshes. We use Bravaislattices or more generallattices with the property that thedegreeof eachinternal vertexis supposedto beconstant. Onsuchmeshes, it is possible todefine the lattice Boltzmannscheme as a discreteparticle 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. 

  • History

Published online: 2013-03

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