On a diphasic low mach number system

Stéphane Dellacherie

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 39, Issue: 3, page 487-514
  • ISSN: 0764-583X

Abstract

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We propose a Diphasic Low Mach Number (DLMN) system for the modelling of diphasic flows without phase change at low Mach number, system which is an extension of the system proposed by Majda in [Center of Pure and Applied Mathematics, Berkeley, report No. 112] and [Combust. Sci. Tech.42 (1985) 185–205] for low Mach number combustion problems. This system is written for a priori any equations of state. Under minimal thermodynamic hypothesis which are satisfied by a large class of generalized van der Waals equations of state, we recover some natural properties related to the dilation and to the compression of bubbles. We also propose an entropic numerical scheme in Lagrangian coordinates when the geometry is monodimensional and when the two fluids are perfect gases. At last, we numerically show that the DLMN system may become ill-posed when the entropy of one of the two fluids is not a convex function.

How to cite

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Dellacherie, Stéphane. "On a diphasic low mach number system." ESAIM: Mathematical Modelling and Numerical Analysis 39.3 (2010): 487-514. <http://eudml.org/doc/194272>.

@article{Dellacherie2010,
abstract = { We propose a Diphasic Low Mach Number (DLMN) system for the modelling of diphasic flows without phase change at low Mach number, system which is an extension of the system proposed by Majda in [Center of Pure and Applied Mathematics, Berkeley, report No. 112] and [Combust. Sci. Tech.42 (1985) 185–205] for low Mach number combustion problems. This system is written for a priori any equations of state. Under minimal thermodynamic hypothesis which are satisfied by a large class of generalized van der Waals equations of state, we recover some natural properties related to the dilation and to the compression of bubbles. We also propose an entropic numerical scheme in Lagrangian coordinates when the geometry is monodimensional and when the two fluids are perfect gases. At last, we numerically show that the DLMN system may become ill-posed when the entropy of one of the two fluids is not a convex function. },
author = {Dellacherie, Stéphane},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Diphasic flow; low mach number system; thermodynamic equilibrium; entropy; van der Waals equations of state.; compressible flows; nuclear reactors; perfect gas; combustion; Navier-Stokes system; van der Waals equations of state; time scales; material waves; acoustic waves; entropic numerical scheme in Lagrangian coordinates; asymptotic expansion; locally well-posed},
language = {eng},
month = {3},
number = {3},
pages = {487-514},
publisher = {EDP Sciences},
title = {On a diphasic low mach number system},
url = {http://eudml.org/doc/194272},
volume = {39},
year = {2010},
}

TY - JOUR
AU - Dellacherie, Stéphane
TI - On a diphasic low mach number system
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 39
IS - 3
SP - 487
EP - 514
AB - We propose a Diphasic Low Mach Number (DLMN) system for the modelling of diphasic flows without phase change at low Mach number, system which is an extension of the system proposed by Majda in [Center of Pure and Applied Mathematics, Berkeley, report No. 112] and [Combust. Sci. Tech.42 (1985) 185–205] for low Mach number combustion problems. This system is written for a priori any equations of state. Under minimal thermodynamic hypothesis which are satisfied by a large class of generalized van der Waals equations of state, we recover some natural properties related to the dilation and to the compression of bubbles. We also propose an entropic numerical scheme in Lagrangian coordinates when the geometry is monodimensional and when the two fluids are perfect gases. At last, we numerically show that the DLMN system may become ill-posed when the entropy of one of the two fluids is not a convex function.
LA - eng
KW - Diphasic flow; low mach number system; thermodynamic equilibrium; entropy; van der Waals equations of state.; compressible flows; nuclear reactors; perfect gas; combustion; Navier-Stokes system; van der Waals equations of state; time scales; material waves; acoustic waves; entropic numerical scheme in Lagrangian coordinates; asymptotic expansion; locally well-posed
UR - http://eudml.org/doc/194272
ER -

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