Geodesic
Mathematical modeling and study of the process of solidification in metal casting
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 5, pp. 882-902 Cet article a éte moissonné depuis la source Math-Net.Ru

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The process of melting and solidification in metal casting is considered. The process is modeled by a three-dimensional two-phase initial-boundary value problem of the Stefan type. The mathematical formulation of the problem and its finite-difference approximation are given. A numerical algorithm is presented for solving the direct problem. The results are described and analyzed in detail. Primary attention is given to the evolution of the solidification front and to how it is affected by the parameters of the problem. Some of the results are illustrated by plots. 
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A. F. Albu; V. I. Zubov. Mathematical modeling and study of the process of solidification in metal casting. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 5, pp. 882-902. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_5_a8/

[1] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1977 | MR | Zbl

[2] Samarskii A. A., Moiseenko B. D., “Ekonomichnaya skhema skvoznogo scheta dlya mnogomernoi zadachi Stefana”, Zh. vychisl. matem. i matem. fiz., 5:5 (1965), 816–827 | MR

[3] Budak B. M., Soloveva E. H., Uspenskii A. B., “Raznostnyi metod so sglazhivaniem koeffitsientov dlya resheniya zadach Stefana”, Zh. vychisl. matem. i matem. fiz., 5:5 (1965), 828–840 | MR | Zbl

[4] Vasilev F. P., “Ob odnom variante metoda pryamykh dlya resheniya zadach tipa Stefana”, Vychisl. metody i programmirovanie, 8, MGU, M., 1967, 139–164

[5] Vasilev F. P., “O metode pryamykh dlya resheniya odnofaznoi zadachi tipa Stefana”, Zh. vychisl. matem. i matem. fiz., 8:1 (1968), 64–78

[6] Bachelis R. D., Melamed V. G., Shlyaifer D. B., “Reshenie zadachi tipa Stefana metodom pryamykh”, Zh. vychisl. matem. i matem. fiz., 9:3 (1969), 585–594 | Zbl

[7] Rose M., “A method for calculating solutions of parabolic equations with a free boundary”, Math. Comput., 14 (1960), 249–256 | DOI | MR | Zbl

[8] White R. E., “An enthalpy formulation of the Stephan problem”, SIAM J. Numer. Analys., 19:6 (1982), 1129–1157 | DOI | MR | Zbl

[9] White R. E., “A numerical solution of the enthalpy formulation of the Stephan problem”, SIAM J. Numer. Analys., 19:6 (1982), 1158–1172 | DOI | MR | Zbl

[10] Darin H. A., Mazhukin V. I., “Matematicheskoe modelirovanie zadachi Stefana na adaptivnoi setke”, Differents. ur-niya, 23:7 (1987), 1154–1160 | MR

[11] Butkovskii A. G., Teoriya optimalnogo upravleniya sistemami s raspredelennymi parametrami, Nauka, M., 1965 | MR

[12] Yurii A. D., “Ob odnoi optimalnoi zadache tipa Stefana”, Dokl. AN SSSR, 251:6 (1980), 1317–1321 | MR

[13] Albu A. F., Gorbunov V. I., Zubov V. I., “Optimalnoe upravlenie protsessom plavleniya”, Zh. vychisl. matem. i matem. fiz., 40:4 (2000), 517–531 | MR | Zbl

[14] Albu A. F., Zubov V. I., “O modifikatsii odnoi skhemy dlya rascheta protsessa plavleniya”, Zh. vychisl. matem. i matem. fiz., 41:9 (2001), 1434–1443 | MR | Zbl

[15] Albu A. F., Zubov V. I., “Optimalnoe upravlenie protsessom kristallizatsii veschestva”, Zh. vychisl. matem. i matem. fiz., 44:1 (2004), 38–50 | MR | Zbl

[16] Albou A. F., Zubov V. I., “Modeling and optimization of melting and solidification process”, Bul. Acad. Stiinte a Republicii Moldova. Matematica, 3(46) (2004), 91–109 | MR | Zbl

[17] Blokh A. G., Osnovy teploobmena izlucheniem, Gosenergoizdat, M., L., 1962

[18] Sperrou E. M., Sess R. D., Teploobmen izlucheniem, “Energiya”, L., 1971