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On the Integro-Differential Radiative Conductive Transfer Equation: A Modified Decomposition Method

In: Integral Methods in Science and Engineering

Author

Listed:
  • Cibele A. Ladeia

    (Federal University of Rio Grande do Sul, Department of Mechanical Engineering)

  • Bardo E. J. Bodmann

    (Federal University of Rio Grande do Sul, Department of Mechanical Engineering)

  • Marco T. Vilhena

    (Federal University of Rio Grande do Sul, Department of Mechanical Engineering)

Abstract

In this work we present a solution for the radiative conductive transfer equation in spherical geometry. We discuss a semi-analytical approach to the non-linear S N problem, where the solution is constructed by Laplace transform and a decomposition method. In the present discussion, we report on arithmetic stability issues for the recursive scheme. In order to stabilise convergence by virtue of limited arithmetic precision, we propose a modification of the Adomian decomposition method by splitting terms responsible for instability by the specific choice of the source terms in the recursive scheme. This procedure results then in a finite number of modified recursion steps controlled by a splitting parameter α, whereas for all subsequent recursion steps the usual recursion scheme is used. Finally, we report on some case studies with numerical results for the solutions and convergence behaviour.

Suggested Citation

  • Cibele A. Ladeia & Bardo E. J. Bodmann & Marco T. Vilhena, 2019. "On the Integro-Differential Radiative Conductive Transfer Equation: A Modified Decomposition Method," Springer Books, in: Christian Constanda & Paul Harris (ed.), Integral Methods in Science and Engineering, chapter 0, pages 197-210, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-16077-7_16
    DOI: 10.1007/978-3-030-16077-7_16
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