Volume 17, Issue 4
Lattice Boltzmann Schemes with Relative Velocities

François Dubois, Tony Fevrier & Benjamin Graille

Commun. Comput. Phys., 17 (2015), pp. 1088-1112.

Published online: 2018-04

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  • Abstract

In this contribution, a new class of lattice Boltzmann schemes is introduced and studied. These schemes are presented in a framework that generalizes the multiple relaxation times method of d’Humières. They extend also the Geier’s cascaded method. The relaxation phase takes place in a moving frame involving a set of moments depending on a given relative velocity field. We establish with the Taylor expansion method that the equivalent partial differential equations are identical to the ones obtained with the multiple relaxation times method up to the second order accuracy. The method is then performed to derive the equivalent equations up to third order accuracy.

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@Article{CiCP-17-1088, author = {François Dubois, Tony Fevrier and Benjamin Graille}, title = {Lattice Boltzmann Schemes with Relative Velocities}, journal = {Communications in Computational Physics}, year = {2018}, volume = {17}, number = {4}, pages = {1088--1112}, abstract = {

In this contribution, a new class of lattice Boltzmann schemes is introduced and studied. These schemes are presented in a framework that generalizes the multiple relaxation times method of d’Humières. They extend also the Geier’s cascaded method. The relaxation phase takes place in a moving frame involving a set of moments depending on a given relative velocity field. We establish with the Taylor expansion method that the equivalent partial differential equations are identical to the ones obtained with the multiple relaxation times method up to the second order accuracy. The method is then performed to derive the equivalent equations up to third order accuracy.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2014.m394}, url = {http://global-sci.org/intro/article_detail/cicp/11003.html} }
TY - JOUR T1 - Lattice Boltzmann Schemes with Relative Velocities AU - François Dubois, Tony Fevrier & Benjamin Graille JO - Communications in Computational Physics VL - 4 SP - 1088 EP - 1112 PY - 2018 DA - 2018/04 SN - 17 DO - http://dor.org/10.4208/cicp.2014.m394 UR - https://global-sci.org/intro/cicp/11003.html KW - AB -

In this contribution, a new class of lattice Boltzmann schemes is introduced and studied. These schemes are presented in a framework that generalizes the multiple relaxation times method of d’Humières. They extend also the Geier’s cascaded method. The relaxation phase takes place in a moving frame involving a set of moments depending on a given relative velocity field. We establish with the Taylor expansion method that the equivalent partial differential equations are identical to the ones obtained with the multiple relaxation times method up to the second order accuracy. The method is then performed to derive the equivalent equations up to third order accuracy.

François Dubois, Tony Fevrier & Benjamin Graille. (1970). Lattice Boltzmann Schemes with Relative Velocities. Communications in Computational Physics. 17 (4). 1088-1112. doi:10.4208/cicp.2014.m394
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