Voir la notice de l'article provenant de la source Numdam
In this paper we present a pressure correction scheme for the compressible Navier-Stokes equations. The space discretization is staggered, using either the Marker-And-Cell (MAC) scheme for structured grids, or a nonconforming low-order finite element approximation for general quandrangular, hexahedral or simplicial meshes. For the energy balance equation, the scheme uses a discrete form of the conservation of the internal energy, which ensures that this latter variable remains positive; this relation includes a numerical corrective term, to allow the scheme to compute correct shock solutions in the Euler limit. The scheme is shown to have at least one solution, and to preserve the stability properties of the continuous problem, irrespectively of the space and time steps. In addition, it naturally boils down to a usual projection scheme in the limit of vanishing Mach numbers. Numerical tests confirm its potentialities, both in the viscous incompressible and Euler limits.
DOI : 10.5802/smai-jcm.9
Keywords: Compressible Navier-Stokes equations, pressure correction schemes, finite volumes, MAC scheme, finite elements.
Grapsas, Dionysis 1 ; Herbin, Raphaèle 1 ; Kheriji, Walid 2 ; Latché, Jean-Claude 2
@article{SMAI-JCM_2016__2__51_0,
author = {Grapsas, Dionysis and Herbin, Rapha\`ele and Kheriji, Walid and Latch\'e, Jean-Claude},
title = {An unconditionally stable staggered pressure correction scheme for the compressible {Navier-Stokes} equations},
journal = {The SMAI Journal of computational mathematics},
pages = {51--97},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {2},
year = {2016},
doi = {10.5802/smai-jcm.9},
mrnumber = {3633545},
zbl = {1416.76149},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5802/smai-jcm.9/}
}
TY - JOUR AU - Grapsas, Dionysis AU - Herbin, Raphaèle AU - Kheriji, Walid AU - Latché, Jean-Claude TI - An unconditionally stable staggered pressure correction scheme for the compressible Navier-Stokes equations JO - The SMAI Journal of computational mathematics PY - 2016 SP - 51 EP - 97 VL - 2 PB - Société de Mathématiques Appliquées et Industrielles UR - http://geodesic.mathdoc.fr/articles/10.5802/smai-jcm.9/ DO - 10.5802/smai-jcm.9 LA - en ID - SMAI-JCM_2016__2__51_0 ER -
%0 Journal Article %A Grapsas, Dionysis %A Herbin, Raphaèle %A Kheriji, Walid %A Latché, Jean-Claude %T An unconditionally stable staggered pressure correction scheme for the compressible Navier-Stokes equations %J The SMAI Journal of computational mathematics %D 2016 %P 51-97 %V 2 %I Société de Mathématiques Appliquées et Industrielles %U http://geodesic.mathdoc.fr/articles/10.5802/smai-jcm.9/ %R 10.5802/smai-jcm.9 %G en %F SMAI-JCM_2016__2__51_0
Grapsas, Dionysis; Herbin, Raphaèle; Kheriji, Walid; Latché, Jean-Claude. An unconditionally stable staggered pressure correction scheme for the compressible Navier-Stokes equations. The SMAI Journal of computational mathematics, Tome 2 (2016), pp. 51-97. doi: 10.5802/smai-jcm.9
Cité par Sources :