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Multigrid Solution of Three-Dimensional Radiative Heat Transfer in Glass Manufacturing

  • M. Seaïd
  • A. Klar
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 8)

Summary

We implement a multigrid algorithm to solve the radiative heat transfer equations in glass production. The time, angle and space coordinates are discretized using Crank-Nicolson, discrete-ordinate and Galerkin methods, respectively. Based on the same mesh hierarchy for both heat conduction and radiative transfer, our multigrid algorithm consists on using the Newton-Gmres and Atkinson-Brakhage solvers as smoothers on the coarse meshes.

Keywords

Radiative Transfer Coarse Mesh Radiative Heat Transfer Multigrid Method Radiative Transfer Equation 
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.
    A. Klar, J. Lang, and M. Seaïd. Adaptive solutions of SPn-approximations to radiative heat transfer in glass. Int. J. Thermal Sciences.Google Scholar
  2. 2.
    E. Larsen, G. Thömmes, A. Klar, M. Seaïd, and Th Götz. Simplified Pn approximations to the equations of radiative heat transfer and applications. J. Comp. Phys., 183:652–675, 2002.CrossRefGoogle Scholar
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    M. Seaïd, M. Frank, A. Klar, R. Pinnau, and G. Thömmes. Efficient numerical methods for radiation in gas turbines. J. Comp. Applied Math., 170:217–239, 2004.CrossRefGoogle Scholar
  4. 4.
    M. Seaïd and A. Klar. Efficient preconditioning of linear systems arising from the discretization of radiative transfer equation. Lecture Notes in Computational Science and Engineering, 35:211–236, 2003.Google Scholar
  5. 5.
    G. Thömmes, R. Pinnau, M. Seaïd, Th. Götz, and A. Klar. Numerical methods and optimal control for glass cooling processes. Transp. Theory Stat. Phys., 31:513–529, 2002.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • M. Seaïd
    • 1
  • A. Klar
    • 1
  1. 1.Fachbereich MathematikTU DarmstadtDarmstadtGermany

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