Numerical simulation of tridimensional electromagnetic shaping of liquid metals

SummaryWe describe a numerical method to compute free surfaces in electromagnetic shaping and levitation of liquid metals. We use an energetic variational formulation and optimization techniques to compute, a critical point. The surfaces are represented by piecewise linear finite elements. Each step of the algorithm requires solving an elliptic boundary value problem in the exterior of the intermediate surfaces. This is done by using an integral representation on these surfaces.

[1]  Antoine Henrot,et al.  Un problème inverse en formage des métaux liquides , 1989 .

[2]  L. R. Scott,et al.  An analysis of quadrature errors in second-kind boundary integral methods , 1989 .

[3]  Olivier Coulaud,et al.  Numerical approximation of a free boundary problem arising in electromagnetic shaping , 1994 .

[4]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[5]  Claude Lemaréchal,et al.  Some numerical experiments with variable-storage quasi-Newton algorithms , 1989, Math. Program..

[6]  J. J. Moré,et al.  Quasi-Newton Methods, Motivation and Theory , 1974 .

[7]  Shmuel S. Oren,et al.  Optimal conditioning of self-scaling variable Metric algorithms , 1976, Math. Program..

[8]  J. Brancher,et al.  Formage d'une lame métallique liquide. Calculs et expériences , 1983 .

[9]  H. K. Moffatt,et al.  Fluid dynamical aspects of the levitation-melting process , 1982, Journal of Fluid Mechanics.

[10]  A. J. Mestel.  Magnetic levitation of liquid metals , 1982, Journal of Fluid Mechanics.

[11]  H. Mittelmann,et al.  The augmented skeleton method for parametrized surfaces of liquid drops , 1989 .

[12]  Kendall E. Atkinson,et al.  A Survey of Boundary Integral Equation Methods for the Numerical Solution of Laplace’s Equation in Three Dimensions , 1990 .

[13]  M. Garnier,et al.  Le problème de frontière libre en lévitation électromagnétique , 1986 .

[14]  A nonlinear boundary value problem solved by spectral methods , 1992 .

[15]  Jean-Paul Zolésio,et al.  The Material Derivative (or Speed) Method for Shape Optimization , 1981 .

[16]  Bo Li,et al.  Computation of shapes of electromagnetically supported menisci in electromagnetic casters. II. Calculations in three dimensions , 1989 .

[17]  H. K. Moffatt,et al.  Deflection of a stream of liquid metal by means of an alternating magnetic field , 1988, Journal of Fluid Mechanics.