@Article{CiCP-34-613,
author = {Dubois , François and Lallemand , Pierre},
title = {On Single Distribution Lattice Boltzmann Schemes for the Approximation of Navier Stokes Equations},
journal = {Communications in Computational Physics},
year = {2023},
volume = {34},
number = {3},
pages = {613--671},
abstract = {<p style="text-align: justify;">In this contribution we study the formal ability of a multi-resolution-times
lattice Boltzmann scheme to approximate isothermal and thermal compressible Navier
Stokes equations with a single particle distribution. More precisely, we consider a total of 12 classical square lattice Boltzmann schemes with prescribed sets of conserved
and nonconserved moments. The question is to determine the algebraic expressions of
the equilibrium functions for the nonconserved moments and the relaxation parameters associated to each scheme. We compare the fluid equations and the result of the
Taylor expansion method at second order accuracy for bidimensional examples with
a maximum of 17 velocities and three-dimensional schemes with at most 33 velocities.
In some cases, it is not possible to fit exactly the physical model. For several examples, we adjust the Navier Stokes equations and propose nontrivial expressions for the
equilibria.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2022-0185},
url = {http://global-sci.org/intro/article_detail/cicp/22020.html}
}