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Finite volume method analysis of heat transfer problem using adapted strongly implicit procedure

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Abstract

In most issues representing physical problems, the complex geometry cannot be represented by a Cartesian grid. The multi-block grid technique allows artificially reducing the complexity of the geometry by breaking down the real domain into a number of sub-domains with simpler geometry. The main aim of this article is to show the usefulness of simple solvers in complex geometry problems, when using curvilinear coordinates combined with multi-block grids. This requires adapted solvers to a nine nodes computational cell instead of the five nodes computational cell used with Cartesian coordinates for two-dimensional cases. These developments are presented for the simple iterative methods Jacobi and Gauss-Seidel and also for the incomplete factorization method strongly implicit procedure (SIP). These adapted solvers are tested in two cases: a simple geometry (heat transfer in a circular cross-section) and a complex geometry (solidification case). Results of the simple geometry case show that all the adapted solvers have good performance with a slight advantage for the SIP solver. For increasing the complexity of the geometry, the results showed that Jacobi and Gauss-Seidel solvers are not suitable. However, the SIP method has a reasonable performance. A conclusion could be drawn that the SIP method could be used in complex geometry problems using multi-block grid technique when high precision results are not required.

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Authors and Affiliations

  1. CITAB-UTAD/Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA, 19104-639, USA

    Abel Rouboa

  2. Engineering Department, University of Trás-os-Montes e Alto Douro, P-5000-911, Vila Real, Portugal

    Eliseu Monteiro

  3. Mathematical Department, University of Trás-os-Montes e Alto Douro, P-5000-911, Vila Real, Portugal

    Regina de Almeida

Authors
  1. Abel Rouboa
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  2. Eliseu Monteiro
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  3. Regina de Almeida
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Corresponding author

Correspondence to Abel Rouboa.

Additional information

This paper was recommended for publication in revised form by Associate Editor Jun Sang Park

Professor Abel Rouboa obtained his P.h.D. (1994) in Fluid Dynamics at University of Paris VI and CEA, before joining the University of Evry Val d’E-ssonne, Paris, as assistant professor. In September 1999, he joined University of UTAD at Vila real, Portugal as assistant professor then in 2003 as associate professor. His teaching interests include heat transfer, fluid mechanics and numerical analysis. Professor Rouboa’s research interests focus on Computational Fluid Dynamics emphasis on heat transfer. Currently, his research works is, strongly, linking with department of Mechanical Engineering and Applied Mechanics of University of Pennsylvania.

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Rouboa, A., Monteiro, E. & de Almeida, R. Finite volume method analysis of heat transfer problem using adapted strongly implicit procedure. J Mech Sci Technol 23, 1553–1562 (2009). https://doi.org/10.1007/s12206-009-0423-3

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  • DOI: https://doi.org/10.1007/s12206-009-0423-3

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