Geodesic
Mathematical modeling of industrial aluminum electrolysis
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 6, pp. 51-61.

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The problem of aluminum electrolysis is discussed. The mathematical model of industrial electrolyzer, presented in the paper is written in the assumption of the electrolyte and metal media immiscibility. In the basis of mathematical statement there is a three-dimensional, nonstationary, and nonlinear system of the magnetic hydrodynamics equations which is written separately in the medium of aluminum and in the medium of electrolyte with the geometry account of wall accretion, skull and arrangement of anodes. The proposed system allows one to model various forms of anodes, number of anodes in a bath and their sizes. Interfaces of media are connected by a viscous friction. Initial values of speeds and electromagnetic fields in the media and the medium interface are considered as the set. On the skull, bottom, and anodes the attachment conditions are set. A speed of change of a magnetic field in the metal and electrolyte on the interface is considered zero. In the basis of a numerical method of the equations system solution there is a well-proved method of division over physical processes. The analysis of the numerical experiment results has shown that it is really possible to allocate “a middle” layer for modeling of the electrolysis process. The proposed model allows to investigate media behavior at occurrence of long anode effect due to sharp reduction of electric conductivity of the electrolyte and subsequent sharp growth of the electric field strength. It is also possible to model occurrence of a hot course of a bath. 
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     author = {R. N. Kuz'min and N. P. Savenkova and A. Ju. Mokin},
     title = {Mathematical modeling of industrial aluminum electrolysis},
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R. N. Kuz'min; N. P. Savenkova; A. Ju. Mokin. Mathematical modeling of industrial aluminum electrolysis. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 6, pp. 51-61. http://geodesic.mathdoc.fr/item/FPM_2009_15_6_a4/

[2] Alatortsev A. V., Kuzmin R. N., Provorova O. G., Savenkova N. P., “Matematicheskaya model magnitno-gidrodinamicheskikh protsessov v alyuminievom elektrolizëre”, Tr. fak. VMiK MGU im. M. V. Lomonosova, 15, 2003, 46–61

[3] Alatortsev A. V., Kuzmin R. N., Provorova O. G., Savenkova N. P., “Dinamicheskaya model magnitno-gidrodinamicheskikh protsessov v alyuminievom elektrolizëre”, Prikl. fiz., 2004, no. 5, 33–42