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

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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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     author = {A. F. Albu and V. I. Zubov},
     title = {Mathematical modeling and study of the process of solidification in metal casting},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
     volume = {47},
     number = {5},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_5_a8/}
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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/