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On the controlling of liquid metal solidification in foundry practice

  • Andrey Albu
  • Vladimir Zubov
Conference paper
Part of the Operations Research Proceedings book series (ORP)

Abstract

The optimal control problem of metal solidification in casting is considered. The process is modeled by a three dimensional two phase initial-boundary value problem of the Stefan type. The optimal control problem was solved numerically using the gradient method. The gradient of the cost function was found with the help of the conjugate problem. The discreet conjugate problem was posed with the help of the Fast Automatic Differentiation technique.

Keywords

Liquid Metal Optimal Control Problem Direct Problem Liquid Aluminum Conjugate Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Albu, A.F., Zubov, V.I.: Mathematical Modeling and Study of the Process of Solidification in Metal Casting. Computational Mathematics and Mathematical Physics 47, 843–862 (2007)CrossRefGoogle Scholar
  2. 2.
    Albu, A.F., Zubov, V.I.: Functional Gradient Evaluation in an Optimal Control Problem Related to Metal Solidification. Computational Mathematics and Mathematical Physics 49, 47–70 (2009)CrossRefGoogle Scholar
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    Albu, A.V., Albu, A.F., Zubov, V.I.: Functional Gradient Evaluation in the Optimal Control of a Complex Dynamical System. Computational Mathematics and Mathematical Physics 51, 762–780 (2011)CrossRefGoogle Scholar
  4. 4.
    Albu, A.V., Zubov, V.I.: Choosing a Cost Functional and a Difference Scheme in the Optimal Control of Metal Solidification. Computational Mathematics and Mathematical Physics 51, 21–34 (2011)CrossRefGoogle Scholar
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    Evtushenko, Y.G.: Computation of Exact Gradients in Distributed Dynamic Systems. Optimizat. Methods and Software 9, 45–75 (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Computing Center RASMoscowRussia

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