Approximation of a solidification problem

• Autorzy: Rajae Aboulaïch , Ilham Haggouch , Ali Souissi
• Języki publikacji: EN

Abstrakty

EN

A two-dimensional Stefan problem is usually introduced as a model of solidification, melting or sublimation phenomena. The two-phase Stefan problem has been studied as a direct problem, where the free boundary separating the two regions is eliminated using a variational inequality (Baiocchi, 1977; Baiocchi et al., 1973; Rodrigues, 1980; Saguez, 1980; Srunk and Friedman, 1994), the enthalpy function (Ciavaldini, 1972; Lions, 1969; Nochetto et al., 1991; Saguez, 1980), or a control problem (El Bagdouri, 1987; Peneau, 1995; Saguez, 1980). In the present work, we provide a new formulation leading to a shape optimization problem. For a semidiscretization in time, we consider an Euler scheme. Under some restrictions related to stability conditions, we prove an L^2 -rate of convergence of order 1 for the temperature. In the last part, we study the existence of an optimal shape, compute the shape gradient, and suggest a numerical algorithm to approximate the free boundary. The numerical results obtained show that this method is more efficient compared with the others.

Słowa kluczowe

EN

free boundary; shape optimization; finite-element method; Euler method; Stefan problem

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2001
• Tom: 11
• Numer: 4
• Strony: 921-955

Daty

wydano

2001

poprawiono

2000-06-17

otrzymano

2000-07-10

(nieznana)

2001-05-24

Twórcy

autor

Rajae Aboulaïch

• Université Mohammed V-Agdal, Ecole Mohammadia d'Ingénieurs, L.E.R.M.A, B.P. 765, Rabat, Morocco

autor

Ilham Haggouch

• Université Mohammed V-Agdal, Ecole Mohammadia d'Ingénieurs, L.E.R.M.A, B.P. 765, Rabat, Morocco

autor

Ali Souissi

• Université Mohammed V-Agdal, Faculté des Sciences, Département de Mathématiques et d’Informatique, B.P. 1014, Rabat, Morocco

Bibliografia

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