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university of Provence - Aix-Marseille I |  |
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university of Provence - Aix-Marseille I | |
| HAL: hal-00692094, version 1 |
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| Numerical Heat Transfer, Part B Fundamentals 60, 5 (2011) 346-369 |
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| Benchmark Solution for a Three-Dimensional Mixed-Convection Flow, Part 2: Analysis of Richardson Extrapolation in the Presence of a Singularity |
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| X. Nicolas 1S. Gounand 2 |
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| (2011-10-28) |
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| Abstract A reference solution to a benchmark problem for a 3D mixed convection flow in a horizontal rectangular channel differentially heated (Poiseuille-Rayleigh-Bénard flow) has been proposed in "Part 1: reference solution" of the present paper [Num. Heat Trans. A, vol.?, pp.?-? (2011)]. Since mixed Dirichlet and Neumann thermal boundary conditions are used on the horizontal walls of the channel, a temperature gradient discontinuity is generated. The aim of this paper is to analyze the consequences of this singularity on Richardson extrapolation (RE) of the numerical solutions. The convergence orders of the used numerical methods (finite difference, finite volume, finite element), observed from RE of local and integral quantities are discussed with an emphasis on singularity influence. With the grids used, it is shown that RE can increase the accuracy of the discrete solutions, preferentially with the discretization methods of low space accuracy order, but only in some part of the channel and for a restricted range of the extrapolation coefficient. A correction to the Taylor expansion involved in the RE formalism is proposed to take into account the singularity and to explain the majority of the RE behaviors observed. |
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| 1: | Laboratoire de Modélisation et Simulation Multi Echelle (MSME) |
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Université Paris-Est Marne-la-Vallée (UPEMLV) – Université Paris-Est Créteil Val-de-Marne (UPEC) – CNRS : UMR8208 |
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| 2: | CEA-Direction de l'Energie Nucléaire (CEA-DEN) |
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CEA |
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| 3: | Institut universitaire des systèmes thermiques industriels (IUSTI) |
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CNRS : UMR6595 – Université de Provence - Aix-Marseille I |
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| 4: | Transferts, écoulements, fluides, énergétique (TREFLE) |
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CNRS : UMR8508 – Université Sciences et Technologies - Bordeaux I – École Nationale Supérieure de Chimie et de Physique de Bordeaux (ENSCPB) – Arts et Métiers ParisTech |
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| CEA-Saclay, DEN, DM2S, SFME, LTMF, Gif-sur-Yvette, France IUSTI, UMR 6595 CNRS, Marseille, France Université de Bordeaux, IPB ENSCBP, CNRS UMR 5295, Institut I2M, Pessac, France |
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| Subject | : | Computer Science/Numerical Analysis Computer Science/Modeling and Simulation Physics/Mechanics/Mechanics of the fluids Engineering Sciences/Mechanics/Fluids mechanics Physics/Mechanics/Thermics Engineering Sciences/Mechanics/Thermics |
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| Richardson extrapolation – singularity – boundary conditions – convergence order – Benchmark – mixed convection – Poiseuille-Rayleigh-Bénard – reference solution |
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| Attached file list to this document: | |||||
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| hal-00692094, version 1 | |
| http://hal-upec-upem.archives-ouvertes.fr/hal-00692094 | |
| oai:hal-upec-upem.archives-ouvertes.fr:hal-00692094 | |
| From: Xavier Nicolas | |
| Submitted on: Friday, 27 April 2012 19:26:19 | |
| Updated on: Friday, 9 November 2012 18:33:20 | |
