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

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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. 

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@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’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. 

}, 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://dor.org/10.4208/cicp.381011.270112s UR - https://global-sci.org/intro/cicp/7241.html KW - AB -

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. 

François Dubois & Pierre Lallemand. (1970). On Triangular Lattice Boltzmann Schemes for Scalar Problems. Communications in Computational Physics. 13 (3). 649-670. doi:10.4208/cicp.381011.270112s
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