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Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium

Gloria FaccanoniSamuel KokhGrégoire Allaire — 2012

ESAIM: Mathematical Modelling and Numerical Analysis

In the present work we investigate the numerical simulation of liquid-vapor phase change in compressible flows. Each phase is modeled as a compressible fluid equipped with its own equation of state (EOS). We suppose that inter-phase equilibrium processes in the medium operate at a short time-scale compared to the other physical phenomena such as convection or thermal diffusion. This assumption provides an implicit definition of an equilibrium EOS...

Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium

Gloria FaccanoniSamuel KokhGrégoire Allaire — 2012

ESAIM: Mathematical Modelling and Numerical Analysis

In the present work we investigate the numerical simulation of liquid-vapor phase change in compressible flows. Each phase is modeled as a compressible fluid equipped with its own equation of state (EOS). We suppose that inter-phase equilibrium processes in the medium operate at a short time-scale compared to the other physical phenomena such as convection or thermal diffusion. This assumption provides an implicit definition of an equilibrium EOS...

Study of a low Mach nuclear core model for two-phase flows with phase transition I: stiffened gas law

Manuel BernardStéphane DellacherieGloria FaccanoniBérénice GrecYohan Penel — 2014

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

In this paper, we are interested in modelling the flow of the coolant (water) in a nuclear reactor core. To this end, we use a monodimensional low Mach number model supplemented with the stiffened gas law. We take into account potential phase transitions by a single equation of state which describes both pure and mixture phases. In some particular cases, we give analytical steady and/or unsteady solutions which provide qualitative information about the flow. In the second part of the paper, we introduce...

A second order anti-diffusive Lagrange-remap scheme for two-component flows

We build a non-dissipative second order algorithm for the approximate resolution of the one-dimensional Euler system of compressible gas dynamics with two components. The considered model was proposed in [1]. The algorithm is based on [8] which deals with a non-dissipative first order resolution in Lagrange-remap formalism. In the present paper we describe, in the same framework, an algorithm that is second order accurate in time and space, and that...

Magnetic equations with FreeFem++: The Grad-Shafranov equation & the current hole

FreeFem++ [11] is a software for the numerical solution of partial differential equations. It is based on finite element method. The FreeFem++ platform aims at facilitating teaching and basic research through prototyping. For the moment this platform is restricted to the numerical simulations of problems which admit a variational formulation. Our goal in this work is to evaluate the FreeFem++ tool on basic magnetic equations arising in Fusion Plasma...

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