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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| Published in: | Journal of mechanical science and technology Vol. 23; no. 6; pp. 1553 - 1562 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Heidelberg
Korean Society of Mechanical Engineers
01.06.2009
Springer Nature B.V 대한기계학회 |
| Subjects: | |
| ISSN: | 1738-494X, 1976-3824 |
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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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| AbstractList | 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. KCI Citation Count: 0 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.[PUBLICATION 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. |
| Author | Rouboa, Abel Monteiro, Eliseu de Almeida, Regina |
| Author_xml | – sequence: 1 givenname: Abel surname: Rouboa fullname: Rouboa, Abel email: rouboa@seas.upenn.edu organization: CITAB-UTAD/Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania – sequence: 2 givenname: Eliseu surname: Monteiro fullname: Monteiro, Eliseu organization: Engineering Department, University of Trás-os-Montes e Alto Douro – sequence: 3 givenname: Regina surname: de Almeida fullname: de Almeida, Regina organization: Mathematical Department, University of Trás-os-Montes e Alto Douro |
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| Cites_doi | 10.1016/j.compstruc.2004.05.021 10.1016/j.cam.2003.05.016 10.1080/01495728108961775 10.1016/j.cma.2003.11.016 10.1137/0705044 10.1016/S0924-0136(97)00449-4 10.1080/10407788708913554 10.1007/BF03177480 10.1016/S1359-4311(01)00068-0 10.1007/BF02984189 10.1115/1.2218352 10.1016/0045-7825(95)00973-6 10.1016/j.cam.2003.09.020 10.1016/S0377-0427(98)00103-4 10.1146/annurev.fluid.29.1.473 10.1016/S0082-0784(81)80144-0 10.1115/1.3450375 10.1007/978-3-642-98037-4 |
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| Copyright | The Korean Society of Mechanical Engineers and Springer-Verlag Berlin Heidelberg 2009 2009 INIST-CNRS The Korean Society of Mechanical Engineers and Springer-Verlag GmbH 2009 |
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| Keywords | 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 |
| Language | English |
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Anal. doi: 10.1137/0705044 – volume: 29 start-page: 473 year: 1997 ident: 423_CR1 publication-title: Annu. Rev. Fluid Mech. doi: 10.1146/annurev.fluid.29.1.473 – volume: 19 start-page: 1773 issue: 9 year: 2005 ident: 423_CR23 publication-title: J. Mech. Sci. Tech. doi: 10.1007/BF02984189 – volume-title: Computational Methods for Fluid Dynamics year: 1999 ident: 423_CR13 doi: 10.1007/978-3-642-98037-4 – volume-title: A Parallel Navier Stokes Solver for Natural convection and Free Surface Flow year: 2001 ident: 423_CR16 – ident: 423_CR15 – volume: 4 start-page: 1 issue: 1 year: 1981 ident: 423_CR11 publication-title: Numer. Heat Transfer. doi: 10.1080/01495728108961775 – volume: 128 start-page: 462 year: 2006 ident: 423_CR22 publication-title: Journal of Pressure Vessel Technology doi: 10.1115/1.2218352 |
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| SubjectTerms | 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 |
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| Title | Finite volume method analysis of heat transfer problem using adapted strongly implicit procedure |
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| Volume | 23 |
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| ispartofPNX | Journal of Mechanical Science and Technology, 2009, 23(6), , pp.1553-1562 |
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