# On a diphasic low Mach number system

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

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topDellacherie, Stéphane. "On a diphasic low Mach number system." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 39.3 (2005): 487-514. <http://eudml.org/doc/245946>.

@article{Dellacherie2005,

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 - Modélisation Mathématique et Analyse Numérique},

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; time scales; material waves; acoustic waves; entropic numerical scheme in Lagrangian coordinates; asymptotic expansion; locally well-posed},

language = {eng},

number = {3},

pages = {487-514},

publisher = {EDP-Sciences},

title = {On a diphasic low Mach number system},

url = {http://eudml.org/doc/245946},

volume = {39},

year = {2005},

}

TY - JOUR

AU - Dellacherie, Stéphane

TI - On a diphasic low Mach number system

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2005

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; time scales; material waves; acoustic waves; entropic numerical scheme in Lagrangian coordinates; asymptotic expansion; locally well-posed

UR - http://eudml.org/doc/245946

ER -

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