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Phase transition with supercooling

A. Fasano (1998)

Bollettino dell'Unione Matematica Italiana

L'articolo riassume il quadro dei risultati noti circa il cosiddetto problema di Stefan con sopraraffreddamento. Con ciò si intende in senso lato l'estensione del modello di Stefan a quei casi in cui la temperatura della fase liquida (solida) non è confinata al di sopra (sotto) di quella di cambiamento di fase, supposta costante. La nostra discussione è prevalentemente rivolta allo sviluppo di singolarità (non limitatezza della velocità dell'interfaccia, ecc.), al modo di prevederle, di prevenirle...

Relaxation models of phase transition flows

Philippe Helluy, Nicolas Seguin (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

In this work, we propose a general framework for the construction of pressure law for phase transition. These equations of state are particularly suitable for a use in a relaxation finite volume scheme. The approach is based on a constrained convex optimization problem on the mixture entropy. It is valid for both miscible and immiscible mixtures. We also propose a rough pressure law for modelling a super-critical fluid.

Segmentation of MRI data by means of nonlinear diffusion

Radomír Chabiniok, Radek Máca, Michal Beneš, Jaroslav Tintěra (2013)

Kybernetika

The article focuses on the application of the segmentation algorithm based on the numerical solution of the Allen-Cahn non-linear diffusion partial differential equation. This equation is related to the motion of curves by mean curvature. It exhibits several suitable mathematical properties including stable solution profile. This allows the user to follow accurately the position of the segmentation curve by bringing it quickly to the vicinity of the segmented object and by approaching the details...

Singular limit of a transmission problem for the parabolic phase-field model

Giulio Schimperna (2000)

Applications of Mathematics

A transmission problem describing the thermal interchange between two regions occupied by possibly different fluids, which may present phase transitions, is studied in the framework of the Caginalp-Fix phase field model. Dirichlet (or Neumann) and Cauchy conditions are required. A regular solution is obtained by means of approximation techniques for parabolic systems. Then, an asymptotic study of the problem is carried out as the time relaxation parameter for the phase field tends to 0 in one of...

Solvability of a class of phase field systems related to a sliding mode control problem

Michele Colturato (2016)

Applications of Mathematics

We consider a phase-field system of Caginalp type perturbed by the presence of an additional maximal monotone nonlinearity. Such a system arises from a recent study of a sliding mode control problem. We prove the existence of strong solutions. Moreover, under further assumptions, we show the continuous dependence on the initial data and the uniqueness of the solution.

Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method

Luise Blank, Martin Butz, Harald Garcke (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The Cahn-Hilliard variational inequality is a non-standard parabolic variational inequality of fourth order for which straightforward numerical approaches cannot be applied. We propose a primal-dual active set method which can be interpreted as a semi-smooth Newton method as solution technique for the discretized Cahn-Hilliard variational inequality. A (semi-)implicit Euler discretization is used in time and a piecewise linear finite element discretization of splitting type is used in space leading...

Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method

Luise Blank, Martin Butz, Harald Garcke (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The Cahn-Hilliard variational inequality is a non-standard parabolic variational inequality of fourth order for which straightforward numerical approaches cannot be applied. We propose a primal-dual active set method which can be interpreted as a semi-smooth Newton method as solution technique for the discretized Cahn-Hilliard variational inequality. A (semi-)implicit Euler discretization is used in time and a piecewise linear finite element discretization of splitting type is used in space...

Some new results on a Stefan problem in a concentrated capacity

Enrico Magenes (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

An existence and uniqueness theorem for a nonlinear parabolic system of partial differential equations, connected with the theory of heat conduction with a transition phase in a concentrated capacity, is given in sufficiently general hypotheses on the data.

Stability and convergence of two discrete schemes for a degenerate solutal non-isothermal phase-field model

Francisco Guillén-González, Juan Vicente Gutiérrez-Santacreu (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

We analyze two numerical schemes of Euler type in time and C0 finite-element type with ℙ 1 -approximation in space for solving a phase-field model of a binary alloy with thermal properties. This model is written as a highly non-linear parabolic system with three unknowns: phase-field, solute concentration and temperature, where the diffusion for the temperature and solute concentration may degenerate. The first scheme is nonlinear, unconditionally stable and convergent. The other scheme is linear...

Stefan problems with a concentrated capacity

Enrico Magenes (1998)

Bollettino dell'Unione Matematica Italiana

Vengono brevemente studiati i problemi di Stefan su «capacità concentrate»,seguendo l'approccio recentemente introdotto di G. Savaré e A. Visintin.

The Effect of Crystal-Melt Surface Energy on the Stability of Ultra-Thin Melt Films

M. Beerman, L. N. Brush (2008)

Mathematical Modelling of Natural Phenomena

The stability and evolution of very thin, single component, metallic-melt films is studied by analysis of coupled strongly nonlinear equations for gas-melt (GM) and crystal-melt (CM) interfaces, derived using the lubrication approximation. The crystal-melt interface is deformable by freezing and melting, and there is a thermal gradient applied across the film. Linear analysis reveals that there is a maximum applied far-field temperature in the gas, beyond which there is no film instability. Instabilities...

The use of linear approximation scheme for solving the Stefan problem

Peter Dzurenda (1997)

Applications of Mathematics

This paper deals with the linear approximation scheme to approximate a singular parabolic problem: the two-phase Stefan problem on a domain consisting of two components with imperfect contact. The results of some numerical experiments and comparisons are presented. The method was used to determine the temperature of steel in the process of continuous casting.

Transizioni di fase ed isteresi

Augusto Visintin (2000)

Bollettino dell'Unione Matematica Italiana

L'attività di ricerca di chi scrive si è finora indirizzata principalmente verso l'esame dei modelli di transizione di fase, dei modelli di isteresi, e delle relative equazioni non lineari alle derivate parziali. Qui si illustrano brevemente tali problematiche, indicando alcuni degli elementi che le collegano tra di loro. Il lavoro è organizzato come segue. I paragrafi 1, 2, 3 vertono sulle transizioni di fase: si introducono le formulazioni forte e debole del classico modello di Stefan, e si illustrano...

Two-stage stochastic programming approach to a PDE-constrained steel production problem with the moving interface

Lubomír Klimeš, Pavel Popela, Tomáš Mauder, Josef Štětina, Pavel Charvát (2017)

Kybernetika

The paper is concerned with a parallel implementation of the progressive hedging algorithm (PHA) which is applicable for the solution of stochastic optimization problems. We utilized the Message Passing Interface (MPI) and the General Algebraic Modelling System (GAMS) to concurrently solve the scenario-related subproblems in parallel manner. The standalone application combining the PHA, MPI, and GAMS was programmed in C++. The created software was successfully applied to a steel production problem...

Currently displaying 101 – 120 of 133