### “A Model for Solving the Maxwell Quasi Stationary Equations in a 3-Phase Electric Reduction Furnace”

**Authors:**S. Ekrann and Terje Sira,

**Affiliation:**International Research Institute of Stavanger (IRIS) and Institute for Energy Technology (IFE)

**Reference:**1982, Vol 3, No 4, pp. 231-242.

**Keywords:**Maxwells quasi-stationary equations, electric and magnetic fields, three-dimensional, numerical methods, finite differences, staggered grid, electric reduction furnace

**Abstract:**A computer code has been developed for the approximate computation of electric and magnetic fields within an electric reduction furnace. The paper describes the numerical methods used to solve Maxwell´s quasi-stationary equations, which are the governing equations for this problem. The equations are discretized by a staggered grid finite difference technique. The resulting algebraic equations are solved by iterating between computations of electric and magnetic quantities. This ´outer´ iteration converges only when the skin depth is larger or of about the same magnitude as the linear dimensions of the computational domain. In solving for electric quantities with magnetic quantities being regarded as known, and vice versa, the central computational task is the solution of a Poisson equation for a scalar potential. These equations are solved by line successive overrelaxation combined with a rebalancing technique.

PDF (2684 Kb) DOI: 10.4173/mic.1982.4.4

**DOI forward links to this article:**

[1] E.M. Rønquist and T. Sira (1984), doi:10.1016/0264-682X(84)90035-2 |

[2] Einar M. Rønquist and Terje Sira (1984), doi:10.4173/mic.1984.2.2 |

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**BibTeX:**

@article{MIC-1982-4-4,

title={{A Model for Solving the Maxwell Quasi Stationary Equations in a 3-Phase Electric Reduction Furnace}},

author={Ekrann, S. and Sira, Terje},

journal={Modeling, Identification and Control},

volume={3},

number={4},

pages={231--242},

year={1982},

doi={10.4173/mic.1982.4.4},

publisher={Norwegian Society of Automatic Control}

};