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

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Progress in Industrial Mathematics at ECMI 2004

Part of the book series: Mathematics in Industry ((TECMI,volume 8))

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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.

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References

  1. A. Klar, J. Lang, and M. Seaïd. Adaptive solutions of SPn-approximations to radiative heat transfer in glass. Int. J. Thermal Sciences.

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  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.

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  3. 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.

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  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.

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  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.

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© 2006 Springer-Verlag Berlin Heidelberg

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Seaïd, M., Klar, A. (2006). Multigrid Solution of Three-Dimensional Radiative Heat Transfer in Glass Manufacturing. In: Di Bucchianico, A., Mattheij, R., Peletier, M. (eds) Progress in Industrial Mathematics at ECMI 2004. Mathematics in Industry, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28073-1_44

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