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

Gloria Faccanoni, Samuel Kokh, Grégoire 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...

Numerical analysis of Eulerian multi-fluid models in the context of kinetic formulations for dilute evaporating sprays

Frédérique Laurent (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

The purpose of this article is the analysis and the development of Eulerian multi-fluid models to describe the evolution of the mass density of evaporating liquid sprays. First, the classical multi-fluid model developed in [Laurent and Massot, Combust. Theor. Model.5 (2001) 537–572] is analyzed in the framework of an unsteady configuration without dynamical nor heating effects, where the evaporation process is isolated, since it is a key issue. The classical multi-fluid method consists then in...

Numerical flux-splitting for a class of hyperbolic systems with unilateral constraint

Florent Berthelin (2003)

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

We study in this paper some numerical schemes for hyperbolic systems with unilateral constraint. In particular, we deal with the scalar case, the isentropic gas dynamics system and the full-gas dynamics system. We prove the convergence of the scheme to an entropy solution of the isentropic gas dynamics with unilateral constraint on the density and mass loss. We also study the non-trivial steady states of the system.

Numerical flux-splitting for a class of hyperbolic systems with unilateral constraint

Florent Berthelin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We study in this paper some numerical schemes for hyperbolic systems with unilateral constraint. In particular, we deal with the scalar case, the isentropic gas dynamics system and the full-gas dynamics system. We prove the convergence of the scheme to an entropy solution of the isentropic gas dynamics with unilateral constraint on the density and mass loss. We also study the non-trivial steady states of the system.

Numerical schemes for a three component Cahn-Hilliard model

Franck Boyer, Sebastian Minjeaud (2011)

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

In this article, we investigate numerical schemes for solving a three component Cahn-Hilliard model. The space discretization is performed by using a Galerkin formulation and the finite element method. Concerning the time discretization, the main difficulty is to write a scheme ensuring, at the discrete level, the decrease of the free energy and thus the stability of the method. We study three different schemes and prove existence and convergence theorems. Theoretical results are illustrated by...

Numerical schemes for a three component Cahn-Hilliard model

Franck Boyer, Sebastian Minjeaud (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

In this article, we investigate numerical schemes for solving a three component Cahn-Hilliard model. The space discretization is performed by using a Galerkin formulation and the finite element method. Concerning the time discretization, the main difficulty is to write a scheme ensuring, at the discrete level, the decrease of the free energy and thus the stability of the method. We study three different schemes and prove existence and convergence theorems. Theoretical results are illustrated by...

Numerical simulation of gluey particles

Aline Lefebvre (2009)

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

We propose here a model and a numerical scheme to compute the motion of rigid particles interacting through the lubrication force. In the case of a particle approaching a plane, we propose an algorithm and prove its convergence towards the solutions to the gluey particle model described in [B. Maury, ESAIM: Proceedings 18 (2007) 133–142]. We propose a multi-particle version of this gluey model which is based on the projection of the velocities onto a set of admissible velocities. Then, we describe...

Numerical simulation of gluey particles

Aline Lefebvre (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose here a model and a numerical scheme to compute the motion of rigid particles interacting through the lubrication force. In the case of a particle approaching a plane, we propose an algorithm and prove its convergence towards the solutions to the gluey particle model described in [B. Maury, ESAIM: Proceedings18 (2007) 133–142]. We propose a multi-particle version of this gluey model which is based on the projection of the velocities onto a set of admissible velocities. Then, we describe...

Numerical simulation of suspension induced rheology

Rodolphe Prignitz, Eberhard Bänsch (2010)

Kybernetika

Flow of particles suspended in a fluid can be found in numerous industrial processes utilizing sedimentation, fluidization and lubricated transport such as food processing, catalytic processing, slurries, coating, paper manufacturing, particle injection molding and filter operation. The ability to understand rheology effects of particulate flows is elementary for the design, operation and efficiency of the underlying processes. Despite the fact that particle technology is widely used, it is still...

On a diphasic low Mach number system

Stéphane Dellacherie (2005)

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

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...

On a diphasic low mach number system

Stéphane Dellacherie (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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...

Currently displaying 81 – 100 of 165