Geodesic
Mathematical model and numerical simulation of aluminum casting and solidification in magnetic fields with allowance for free surface dynamics
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 12, pp. 2094-2108

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A complex mathematical model of aluminum casting and solidification in a variable electromagnetic field is constructed. The model is based on the solution of magnetohydrodynamic equations and the VOF method. Test results are presented for the model and the numerical algorithm proposed. The numerical results are compared with experimental data and computations of other authors and are found to be in good agreement. The model is used to simulate aluminum solidification under an electromagnetic field. The physical processes influencing ingot formation are analyzed. 
@article{ZVMMF_2015_55_12_a11,
     author = {A. V. Minakov and M. V. Pervukhin and D. V. Platonov and M. Yu. Khatsayuk},
     title = {Mathematical model and numerical simulation of aluminum casting and solidification in magnetic fields with allowance for free surface dynamics},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2094--2108},
     publisher = {mathdoc},
     volume = {55},
     number = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a11/}
}
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A. V. Minakov; M. V. Pervukhin; D. V. Platonov; M. Yu. Khatsayuk. Mathematical model and numerical simulation of aluminum casting and solidification in magnetic fields with allowance for free surface dynamics. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 12, pp. 2094-2108. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a11/