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1 results

  • On Triangular Lattice Boltzmann Schemes for Scalar Problems

  • François Dubois, Pierre Lallemand
  • Journal:
    Communications in Computational Physics / Volume 13 / Issue 3 / March 2013
    Published online by Cambridge University Press:
    03 June 2015, pp. 649-670
    Print publication:
    March 2013

  • 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.