On triangular lattice Boltzmann schemes for scalar problems

François Dubois (1, 2) , Pierre Lallemand (3)

1 LMSSC - Laboratoire de Mécanique des Structures et des Systèmes Couplés
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 CSRC - Beijing Computational Science Research Center [Beijing]

We propose to extend the d'Humiéres 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.

Mots clés: Laplacian operator; heat equation; d'Humiéres scheme

Domaines: Analyse numérique [math.NA]; Thermique [physics.class-ph]; Thermique [physics.class-ph]

François Dubois, Pierre Lallemand. On triangular lattice Boltzmann schemes for scalar problems. Communications in Computational Physics, 2013, 13 (3), pp.649-670. ⟨10.4208/cicp.381011.270112s⟩. ⟨hal-00986779⟩