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Numerical simulation of steel solidification in continuous casting

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Abstract

The present study deals with the numerical simulation of steel solidification in continuous casting. We consider a semi-discretization with respect to the time of the studied evolution problem; then we have to solve a sequence of stationary coupled problems. So, due to the fact that the temperature is assumed to be positive, after reformulation of the problem into a variational inequality, we study under appropriate assumptions the existence and uniqueness of the solution of the stationary coupled problems. We also consider a multivalued formulation of the same problem which allows to analyze the behavior of the iterative relaxation algorithms used for the solution of the discretized problems. Finally the numerical experiments are presented.

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Notes

  1. i.e. a proper function from V to \( ]- \infty , + \infty ]\) not identically equal to \(+ \infty \).

  2. i.e. a bilinear form, from \(V \times {V}^{\prime }\) onto \(\mathfrak {R}\).

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Acknowledgments

This study was possible thanks to a grant conceded to Miss Ghania Khenniche by the Algerian govermment. Also Miss Ghania Khenniche gratefully acknowledges support provided by the National Polytechnic Institute of Toulouse and the Institute of Research and computer science of Toulouse during her stage in France.

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Authors and Affiliations

  1. Laboratory LAMAHIS, Department of Mathematics, Faculty of sciences, University 20 August 1955, Skikda, Algeria

    Ghania Khenniche

  2. Laboratory IRIT-INP-ENSEEIHT, 2 rue Charles Camichel, 31071, Toulouse CEDEX, France

    Ghania Khenniche & Pierre Spiteri

  3. Welding and NDT Research Centre, Iron and Steel Applied Research Unit-CSC, BP 196, 23000, Annaba, Algeria

    Salah Bouhouche

  4. Laboratory LANOS, Badji Mokhtar University, PO Box 12, 23000, Annaba, Algeria

    Hocine Sissaoui

Authors
  1. Ghania Khenniche
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  2. Pierre Spiteri
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  3. Salah Bouhouche
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  4. Hocine Sissaoui
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Corresponding author

Correspondence to Pierre Spiteri.

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Khenniche, G., Spiteri, P., Bouhouche, S. et al. Numerical simulation of steel solidification in continuous casting. Afr. Mat. 28, 417–441 (2017). https://doi.org/10.1007/s13370-016-0454-8

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  • DOI: https://doi.org/10.1007/s13370-016-0454-8

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