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

François Dubois & Pierre Lallemand

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

Published online: 2013-03

Preview Full PDF 278 2634
Export citation
  • Abstract

We propose to extend the d'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.

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-13-649, author = {}, title = {On Triangular Lattice Boltzmann Schemes for Scalar Problems}, journal = {Communications in Computational Physics}, year = {2013}, volume = {13}, number = {3}, pages = {649--670}, abstract = {

We propose to extend the d'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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.381011.270112s}, url = {http://global-sci.org/intro/article_detail/cicp/7241.html} }
TY - JOUR T1 - On Triangular Lattice Boltzmann Schemes for Scalar Problems 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 -

We propose to extend the d'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.

François Dubois & Pierre Lallemand. (2020). On Triangular Lattice Boltzmann Schemes for Scalar Problems. Communications in Computational Physics. 13 (3). 649-670. doi:10.4208/cicp.381011.270112s
Copy to clipboard
The citation has been copied to your clipboard