TY - JOUR
T1 - On Triangular Lattice Boltzmann Schemes for Scalar Problems
AU - François Dubois & Pierre Lallemand
JO - Communications in Computational Physics
VL - 3
SP - 649
EP - 670
PY - 2013
DA - 2013/03
SN - 13
DO - http://doi.org/10.4208/cicp.381011.270112s
UR - https://global-sci.org/intro/article_detail/cicp/7241.html
KW - 
AB - <p style="text-align: justify;">We propose to extend the d&#39;Humières 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.</p>