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Afrika Matematika

, Volume 28, Issue 3–4, pp 417–441 | Cite as

Numerical simulation of steel solidification in continuous casting

  • Ghania Khenniche
  • Pierre SpiteriEmail author
  • Salah Bouhouche
  • Hocine Sissaoui
Article
  • 137 Downloads

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.

Keywords

Continuous casting Solidification of steel Sparse nonlinear systems Relaxation method 

Mathematics Subject Classification

58J35 35B09 58J26 35R70 

Notes

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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Copyright information

© African Mathematical Union and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Ghania Khenniche
    • 1
    • 2
  • Pierre Spiteri
    • 2
    Email author
  • Salah Bouhouche
    • 3
  • Hocine Sissaoui
    • 4
  1. 1.Laboratory LAMAHIS, Department of Mathematics, Faculty of sciencesUniversity 20 August 1955SkikdaAlgeria
  2. 2.Laboratory IRIT-INP-ENSEEIHTToulouse CEDEXFrance
  3. 3.Welding and NDT Research CentreIron and Steel Applied Research Unit-CSCAnnabaAlgeria
  4. 4.Laboratory LANOSBadji Mokhtar UniversityAnnabaAlgeria

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