Singularities in a two-fluid medium.
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Solutions of a nonhyperbolic pair of balance laws
Michael Sever (2005)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
We describe a constructive algorithm for obtaining smooth solutions of a nonlinear, nonhyperbolic pair of balance laws modeling incompressible two-phase flow in one space dimension and time. Solutions are found as stationary solutions of a related hyperbolic system, based on the introduction of an artificial time variable. As may be expected for such nonhyperbolic systems, in general the solutions obtained do not satisfy both components of the given initial data. This deficiency may be overcome,...
Solutions of a nonhyperbolic pair of balance laws
Michael Sever (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
We describe a constructive algorithm for obtaining smooth solutions of a nonlinear, nonhyperbolic pair of balance laws modeling incompressible two-phase flow in one space dimension and time. Solutions are found as stationary solutions of a related hyperbolic system, based on the introduction of an artificial time variable. As may be expected for such nonhyperbolic systems, in general the solutions obtained do not satisfy both components of the given initial data. This deficiency may be overcome,...
Some recent results on the Muskat problem
Angel Castro, Diego Córdoba, Francisco Gancedo (2010)
Journées Équations aux dérivées partielles
We consider the dynamics of an interface given by two incompressible fluids with different characteristics evolving by Darcy’s law. This scenario is known as the Muskat problem, being in 2D mathematically analogous to the two-phase Hele-Shaw cell. The purpose of this paper is to outline recent results on local existence, weak solutions, maximum principles and global existence.
Spectral element simulations of flow past an ellipsoid at different Reynolds numbers.
Liu, Don, Karniadakis, George, Maxey, Martin (2009)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit
Giovanni Naldi, Lorenzo Pareschi, Giuseppe Toscani (2003)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
In this paper we introduce numerical schemes for a one-dimensional kinetic model of the Boltzmann equation with dissipative collisions and variable coefficient of restitution. In particular, we study the numerical passage of the Boltzmann equation with singular kernel to nonlinear friction equations in the so-called quasi elastic limit. To this aim we introduce a Fourier spectral method for the Boltzmann equation [25, 26] and show that the kernel modes that define the spectral method have the correct...
Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit
Giovanni Naldi, Lorenzo Pareschi, Giuseppe Toscani (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
In this paper we introduce numerical schemes for a one-dimensional kinetic model of the Boltzmann equation with dissipative collisions and variable coefficient of restitution. In particular, we study the numerical passage of the Boltzmann equation with singular kernel to nonlinear friction equations in the so-called quasi elastic limit. To this aim we introduce a Fourier spectral method for the Boltzmann equation [CITE] and show that the kernel modes that define the spectral method have the correct...
Study of a low Mach nuclear core model for two-phase flows with phase transition I: stiffened gas law
Manuel Bernard, Stéphane Dellacherie, Gloria Faccanoni, Bérénice Grec, Yohan 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...
Study of a three component Cahn-Hilliard flow model
Franck Boyer, Céline Lapuerta (2006)
ESAIM: Mathematical Modelling and Numerical Analysis
In this paper, we propose a new diffuse interface model for the study of three immiscible component incompressible viscous flows. The model is based on the Cahn-Hilliard free energy approach. The originality of our study lies in particular in the choice of the bulk free energy. We show that one must take care of this choice in order for the model to give physically relevant results. More precisely, we give conditions for the model to be well-posed and to satisfy algebraically and dynamically consistency...
Sulla dinamica di una miscela di due fluidi comprimibili e non miscibili
Pasquale Giovine (1990)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
Si dà un ulteriore contributo alla specificazione delle equazioni dinamiche di bilancio per una miscela di due fluidi non miscibili ma comprimibili.
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