Besson, O.; Bourgeois, J.; Chevalier, P.-A.; Rappaz, J.; Touzani, R. Numerical modelling of electromagnetic casting processes. (English) Zbl 0721.65076 J. Comput. Phys. 92, No. 2, 482-507 (1991). Electromagnetic casting leads to a mathematical model that consists from electromagnetics coupled with hydrodynamics with one free boundary. This model can be solved by the following proposed algorithm: (1) give an initial meniscus shape, (2) solve Maxwell’s equations and compute Lorentz forces, (3) solve Navier-Stokes equations and compute normal tractions on the meniscus, (4) update the meniscus, (5) if the meniscus shape is “sufficiently close” to the previous one, then stop; otherwise, go to 2. Reviewer: I.Grosu (Iaşi) Cited in 16 Documents MSC: 65Z05 Applications to the sciences 35Q30 Navier-Stokes equations 35Q60 PDEs in connection with optics and electromagnetic theory 80A20 Heat and mass transfer, heat flow (MSC2010) 78A55 Technical applications of optics and electromagnetic theory Keywords:Electromagnetic casting; free boundary; Maxwell’s equations; Lorentz forces; Navier-Stokes equations PDFBibTeX XMLCite \textit{O. Besson} et al., J. Comput. Phys. 92, No. 2, 482--507 (1991; Zbl 0721.65076) Full Text: DOI References: [1] Weber, J. C.; Buxmann, K.; Von Kaenel, R.; Plata, M., (Boxall, L. G., Light Metals (1988), The Metallurgical Society: The Metallurgical Society Warrendale, PA), 503 [2] Sakane, J.; Li, B. Q.; Evans, J. W., Metall. Trans. B, 19B, 397 (1988) [3] Glière, A.; Massé, P.; Fautrelle, Y., IEEE Trans. Magn., MAG-24, 1 (1988) [4] Bqssavit, A., Comput. Methods Appl. Mech. Eng., 27, 303 (1981) [5] Landau, L.; Lifschitz, E., Electrodynamics of Continuous Media (1960), Pergamon: Pergamon London [6] Johnson, C.; Nedelec, J.-C., Math. Comput., 35, 1063 (1980) [7] Zienkiewicz, O.; Kelly, D. W.; Bettess, P., Int. J. Num. Methods Eng., 11, 355 (1977) [8] Nedelec, J.-C., Approximation des équations intégrales en mécanique et en physique (1977), Centre de Mathématiques Appliquées, Ecole Polytechnique: Centre de Mathématiques Appliquées, Ecole Polytechnique Palaiseau, (unpublished) [9] Crouzeix, M.; Descloux, J., SIAM J. Math. Anal., 21, No. 3, 577 (1990) [10] Bossavit, A.; Vérité, J.-C., IEEE Trans. Magn., MAG-19, No. 6, 2465 (1983) [11] Hughes, T. J.R.; Liu, W. K.; Brooks, A., J. Comput. Phys., 30, 1 (1979) [12] Utku, M.; Carey, G. F., Comput. Methods Appl. Mech. Eng., 30, 103 (1982) [13] Cuvelier, C., Some Numerical Methods for the Computation of Capillary Free Boundaries Governed by the Navier-Stokes Equations, Technical Report 87-69 (1987), (unpublished) · Zbl 0706.76027 [14] Landau, L.; Lifchitz, E., Fluid Mechanics (1959), Pergamon: Pergamon London This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.