[Une méthode cinématique de pénalité–projection vectorielle pour l'écoulement incompressible à densité variable]
On présente dans cette Note une nouvelle version de la méthode de splitting par pénalité–projection vectorielle décrite dans [1] pour le calcul des écoulements incompressibles à masse volumique et viscosité variables. Le principal résultat est de rendre la correction vectorielle de vitesse complètement indépendante de la masse volumique ρ. Cette étape devient donc purement cinématique et correspond à une décomposition rapide de Helmholtz–Hodge proposée dans [2]. On montre que l'étape dynamique de correction du gradient de pression peut être rapide et localement consistante sur des maillages généralisés de type MAC non structurés.
In this Note, we present a new version of the vector penalty–projection splitting method described in [1] for the fast numerical computation of incompressible flows with variable density and viscosity. We show that the velocity correction can be made completely independent of the mass density ρ. Hence, this step is purely kinematic using the fast Helmholtz–Hodge decompositions proposed in [2]. Then, it is shown that the dynamic step of pressure gradient correction can be fast and locally consistent on edge-based generalized MAC-type unstructured meshes that naturally verify the compatibility condition in the proposed discrete setting. By the way, a new accurate front-tracking Lagrangian-advection technique is also introduced for multiphase flows.
This new method preserves the fully vector formulation of both the prediction and correction steps of the original scheme, the primary unknowns being and ρ by advection, since the pressure Neumann–Poisson problem remains eliminated. The efficiency of the present method is demonstrated through numerical results on sharp test cases.
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@article{CRMATH_2016__354_11_1124_0,
author = {Angot, Philippe and Caltagirone, Jean-Paul and Fabrie, Pierre},
title = {A kinematic vector penalty{\textendash}projection method for incompressible flow with variable density},
journal = {Comptes Rendus. Math\'ematique},
pages = {1124--1131},
publisher = {Elsevier},
volume = {354},
number = {11},
year = {2016},
doi = {10.1016/j.crma.2016.06.007},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2016.06.007/}
}
TY - JOUR AU - Angot, Philippe AU - Caltagirone, Jean-Paul AU - Fabrie, Pierre TI - A kinematic vector penalty–projection method for incompressible flow with variable density JO - Comptes Rendus. Mathématique PY - 2016 SP - 1124 EP - 1131 VL - 354 IS - 11 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2016.06.007/ DO - 10.1016/j.crma.2016.06.007 LA - en ID - CRMATH_2016__354_11_1124_0 ER -
%0 Journal Article %A Angot, Philippe %A Caltagirone, Jean-Paul %A Fabrie, Pierre %T A kinematic vector penalty–projection method for incompressible flow with variable density %J Comptes Rendus. Mathématique %D 2016 %P 1124-1131 %V 354 %N 11 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2016.06.007/ %R 10.1016/j.crma.2016.06.007 %G en %F CRMATH_2016__354_11_1124_0
Angot, Philippe; Caltagirone, Jean-Paul; Fabrie, Pierre. A kinematic vector penalty–projection method for incompressible flow with variable density. Comptes Rendus. Mathématique, Tome 354 (2016) no. 11, pp. 1124-1131. doi : 10.1016/j.crma.2016.06.007. http://www.numdam.org/articles/10.1016/j.crma.2016.06.007/
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