In this paper we introduce a new class of numerical schemes for the incompressible Navier-Stokes equations, which are inspired by the theory of discrete kinetic schemes for compressible fluids. For these approximations it is possible to give a stability condition, based on a discrete velocities version of the Boltzmann H-theorem. Numerical tests are performed to investigate their convergence and accuracy.
Mots-clés : incompressible fluids, kinetic schemes, BGK models, finite difference schemes
@article{M2AN_2008__42_1_93_0,
author = {Carfora, Maria Francesca and Natalini, Roberto},
title = {A discrete kinetic approximation for the incompressible {Navier-Stokes} equations},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {93--112},
publisher = {EDP-Sciences},
volume = {42},
number = {1},
year = {2008},
doi = {10.1051/m2an:2007055},
mrnumber = {2387423},
zbl = {1135.76037},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2007055/}
}
TY - JOUR AU - Carfora, Maria Francesca AU - Natalini, Roberto TI - A discrete kinetic approximation for the incompressible Navier-Stokes equations JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2008 SP - 93 EP - 112 VL - 42 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2007055/ DO - 10.1051/m2an:2007055 LA - en ID - M2AN_2008__42_1_93_0 ER -
%0 Journal Article %A Carfora, Maria Francesca %A Natalini, Roberto %T A discrete kinetic approximation for the incompressible Navier-Stokes equations %J ESAIM: Modélisation mathématique et analyse numérique %D 2008 %P 93-112 %V 42 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2007055/ %R 10.1051/m2an:2007055 %G en %F M2AN_2008__42_1_93_0
Carfora, Maria Francesca; Natalini, Roberto. A discrete kinetic approximation for the incompressible Navier-Stokes equations. ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 1, pp. 93-112. doi : 10.1051/m2an:2007055. http://www.numdam.org/articles/10.1051/m2an:2007055/
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