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

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...

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Bibliographic Details
Published in:Journal of mechanical science and technology Vol. 23; no. 6; pp. 1553 - 1562
Main Authors: Rouboa, Abel, Monteiro, Eliseu, de Almeida, Regina
Format: Journal Article
Language:English
Published: Heidelberg Korean Society of Mechanical Engineers 01.06.2009
Springer Nature B.V
대한기계학회
Subjects:
Analytical and numerical techniques
Complexity
Computation
Computational techniques
Condensed matter: structure, mechanical and thermal properties
Control
Coordinates
Cross sections
Dynamical Systems
Engineering
Equations of state, phase equilibria, and phase transitions
Exact sciences and technology
Factorization
Finite volume method
Fundamental areas of phenomenology (including applications)
Geometry
Heat transfer
Industrial and Production Engineering
Mathematical methods in physics
Mechanical Engineering
Physics
Solid-liquid transitions
Solidification
Solvers
Specific phase transitions
Studies
Vibration
기계공학
Strongly implicit procedure
Curvilinear coordinates
Multi-block grid
Heat transfer
Jacobi method
Gauss method
Finite volume methods
Solidification
Temperature effects
Multigrid
Factorization method
Modelling
Iterative methods
Domain decomposition
Gauss Seidel method
Cartesian coordinates
ISSN:1738-494X, 1976-3824
Online Access:Get full text
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Summary: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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G704-000058.2009.23.6.001
ISSN:1738-494X
1976-3824
DOI:10.1007/s12206-009-0423-3