Publication Cover
Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 60, 2011 - Issue 5
250
Views
12
CrossRef citations to date
0
Altmetric
Original Articles

Benchmark Solution for a Three-Dimensional Mixed-Convection Flow, Part 1: Reference Solutions

, , &
Pages 325-345 | Received 18 Mar 2011, Accepted 06 Aug 2011, Published online: 28 Oct 2011

REFERENCES

  • X. Nicolas , A. Benzaoui , and S. Xin , Numerical Simulation of Thermoconvective Flows and More Uniform Depositions in a Cold Wall Rectangular APCVD Reactor , J. Crystal Growth , vol. 310 , pp. 174 – 186 , 2008 .
  • Q. H. Wang and Y. Jaluria , Instability and Heat Transfer in Mixed-Convection Flow in a Horizontal Duct with Discrete Heat Sources, Numer. Heat Transfer A , vol. 42, pp. 445–463, 2002.
  • X. Nicolas , Bibliographical Review on the Poiseuille-Rayleigh-Bénard Flows: The Mixed Convection Flows in Horizontal Rectangular Ducts Heated from Below , Int. J. Thermal Sci. , vol. 41 , pp. 961 – 1016 , 2002 .
  • H. Ben Hamed , R. Bennacer , T. Langlet , H. Sammouda , and H. Béji , Numerical 3D-Study of Poiseuille Rayleigh Benard Soret Problem in a Finite Extent Paralellepipedic Duct , Numer. Heat Transfert A , vol. 55 , pp. 534 – 552 , 2009 .
  • O. Rahli , R. Bennacer , K. Bouhadef , and D. E. Ameziani , Three-Dimensional Mixed Convection Heat and Mass Transfer in a Rectangular Duct: Case of Longitudinal Rolls , Numer. Heat Transfer A , vol. 59 , pp. 349 – 371 , 2011 .
  • K. C. Chiu and F. Rosenberger , Mixed Convection between Horizontal Plates—1: Entrance Effects , Int. J. Heat Mass Transfer , vol. 30 , pp. 1645 – 1654 , 1987 .
  • M. T. Ouazzani , J. K. Platten , and A. Mojtabi , Etude Expérimentale de la Convection Mixte Entre Deux Plans Horizontaux à Températures Différentes—2 , Int. J. Heat Mass Transfer , vol. 33 , pp. 1417 – 1427 , 1990 .
  • A. Benzaoui , X. Nicolas , and S. Xin , Efficient Vectorized Finite Difference Method to Solve the Incompressible Navier-Stokes Equations for 3D Mixed Convection Flows in High Aspect Ratio Channels , Numer. Heat Transfer B , vol. 48 , pp. 277 – 302 , 2005 .
  • M. Medale and X. Nicolas , CALL FOR CONTRIBUTIONS: Towards Numerical Benchmark Solutions for 3D Mixed Convection Flows in Rectangular Channels Heated from Below , Int. J. Thermal Sci. , vol. 45 , pp. 331 – 333 , 2006 .
  • K. F. Alvin , W. L. Oberkampf , B. M. Rutherford , and K. V. Diegert , Methodology for Characterizing Modeling and Discretization Uncertainties in Computational Simulation (read §4, pp. 28–37), SAND2000-0515 , Sandia Natl. Labor. , Albuquerque , NM , 2000 .
  • P. J. Roache , Perspective: A Method for Uniform Reporting of Grid Refinement Studies , J. Fluids Eng. , vol. 116 , pp. 405 – 413 , 1994 .
  • W. L. Oberkampf and T. Trucano , Verification, and Validation in Computational Fluid Dynamics (read §3.3, pp. 31–42), SAND2002-0529, Sandia Natl. Labor., Albuquerque, NM, 2002, also in Prog. Aerospace Sci. , vol. 38 , pp. 209 – 272 , 2002 .
  • C. J. Roy , Review of Code and Solution Verification Procedures for Computational Simulation , J. Comput. Phys. , vol. 205 , pp. 131 – 156 , 2005 .
  • H. Pabiou , S. Mergui , and C. Bénard , Wavy Secondary Instability of Longitudinal Rolls in Rayleigh–Bénard–Poiseuille Flows , J. Fluid Mech. , vol. 542 , pp. 175 – 194 , 2005 .
  • X. Nicolas , S. Gounand , M. Medale , and S. Glockner , Benchmark Solution for a Three-Dimensional Mixed Convection Flow - Part 2: Analysis of Richardson Extrapolation in the Presence of a Singularity , Numer. Heat Transfer B , vol. 60 , pp. 346 – 369 , 2011 .
  • X. Nicolas , J. M. Luijkx , and J. K. Platten , Linear Stability of Mixed Convection Flows in Horizontal Rectangular Channels of Finite Transversal Extension Heated from below , Int. J. Heat Mass Transfer , vol. 43 , pp. 589 – 610 , 2000 .
  • K. Goda , A Multistep Technique with Implicit Difference Schemes for Calculating Two- or Three-Dimensional Cavity Flows , J. Comput. Phys. , vol. 30 , pp. 76 – 95 , 1979 .
  • J. L. Guermond and J. Shen , A New Class of Truly Consistent Splitting Schemes for Incompressible Flows , J. Comput. Phys. , vol. 192 , pp. 262 – 276 , 2003 .
  • S. A. Orszag , M. Israeli , and M. O. Deville , Boundary Conditions for Incompressible Flows , J. Sci. Comput. , vol. 1 , pp. 75 – 111 , 1986 .
  • G. E. M. Karniadakis , M. Israeli , and S. A. Orszag , High-Order Splitting Methods for the Incompressible Navier-Stokes Equations , J. Comput. Phys. , vol. 97 , pp. 414 – 443 , 1991 .
  • T. C. Papanastasiou , N. Malamataris , and K. Ellwood , A New Outflow Boundary Condition, Int. J. Numer. Meth. Fluids , vol. 14, pp. 587–608, 1992.
  • S. Balay , K. Buschelman , W. D. Gropp , D. Kaushik , M. G. Knepley , L. Curfman McInnes , B. F. Smith , and H. Zhang , Petsc Web pages, www.mcs.anl.gov/petsc , 2007 .
  • L. J. P. Timmermans , P. D. Minev , and F. N. Van De Vosse , An Approximate Projection Scheme for Incompressible Flow Using Spectral Elements , Int. J. Numer. Meth. Fluids , vol. 22 , pp. 673 – 688 , 1996 .
  • B. P. Leonard , A Stable and Accurate Convection Modelling Procedure Based on Quadratic Upstream Interpolation , Comput. Meth. Appl. Mech. Eng. , vol. 19 , pp. 59 – 98 , 1979 .
  • E. Ahusborde and S. Glockner , A 2D Block-Structured Mesh Partitioner for Accurate Flow Simulations on Non-Rectangular Geometries , Comput. Fluids , vol. 43 , pp. 2 – 13 , 2011 .
  • R. D. Falgout , J. E. Jones , and U. M. Yang , The Design and Implementation of Hypre, a Library of Parallel High Performance Preconditioners , in A. M. Bruaset and A. Tveito , (eds.), Numerical Solution of Partial Differential Equations on Parallel Computers , Springer-Verlag , UCRL-JRNL-205459 , vol. 51 , pp. 267 – 294 , 2006 .
  • A. Ern and J. L. Guermond , Theory and Practice of Finite Elements , Applied Mathematical Series , vol. 159 , chap. 4 , Springer-Verlag , New-York , 2004 .
  • S. Turek , Efficient Solvers for Incompressible Flow Problems—An Algorithmic and Computational Approach , Lecture Notes in Computational Science and Engineering , vol. 6 , chap. 3 , Springer-Verlag , Berlin , 1999 .
  • A. Quarteroni , F. Saleri , and A. Veneziani , Factorization Methods for the Numerical Approximation of Navier-Stokes Equations , CNAME , vol. 188 , pp. 505 – 526 , 2000 .
  • Y. Saad , Iterative Methods for Sparse Linear Systems, , 2d ed. , chaps. 8 and 10 , SIAM , Philadelphia , 2003 .
  • Y. Notay , An Aggregation-Based Algebraic Multigrid Method , Electron. Trans. Numer. Anal. , vol. 37 , pp. 123 – 146 , 2010 .
  • Cast3m website, www-cast3m.cea.fr.
  • X. Nicolas , M. Medale , S. Gounand , and S. Glockner , Benchmark Solution for a Three-Dimensional Mixed Convection Flow—Detailed Technical Report, www.sft.asso.fr/Local/sft/dir/user-3775/documents/DocumentsDivers/SFT_Report_benchmark_PRB_2011.pdf, pp. 1–44 , 2011 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.