Calculation of the Electromagnetic Field and Melt Shape in Electromagnetic Confinement Systems: A Comparison between Numerical Methods

"Numerical simulation of electromagnetic confinement systems generally requires large CPU time due to the strong coupling between the electromagnetic and the free boundary problems. The present paper examines the accuracy and the computational efficiency of the most common numerical schemes used in modeling such systems. Levitation melting was taken as a test case. In this study, a comparison was made between the finite element and surface integral methods for electromagnetic field calculations. The computational efficiency of Lagrange and the modified Hestenes methods for solving the free boundary problem were investigated. The convergence of the Lagrange method was found to be much faster than the modified Hestenes method. It was also found that finite element method not only gives accurate solutions, but faster convergence to the final equilibrium shape than the surface integral method. The applications and the limitations of these techniques in modeling electromagnetic confinement systems will be discussed.IntroductionIn recent years there has been a growing interest in the use of electromagnetic forces for confinement of molten metals as a means to eliminate molten metal contamination during melting and to improve surface quality of cast products. Continuous casting of metal without contact of a mold is now a reality, and is being commercially applied for casting of aluminum slabs /1/, and copper rods /2/. New applications of electromagnetic confinement in melting and casting include containerless melting (Magnetic Suspension Melting) /3/, edge containment in twin roll casting, and meniscus shape control in continuous casting of steel /4/.Modeling of confinement systems involves the determination of the electromagnetic field and the equilibrium shape. These two problems are strongly coupled due to the dependence of the field on the shape of the melt. While significant advances have been made in computational electromagnetics /5/, the application of developed computational techniques to electromagnetic confinement problems is not a simple task. The principal difficulty in using these methods is that the solution domain is not known a priori. due to coupling between the electromagnetic field and the free boundary problems. These two problems have to be solved simultaneously, leading to an iterative solution procedure. As a result, numerical simulation of electromagnetic confinement systems are computationally intensive with computational time at least an order of magnitude larger than the fixed domain problems."