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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 68, 2015 - Issue 4
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Original Articles

A Dimension Splitting Method for 3-D Incompressible Thermal Flow

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Pages 336-365 | Received 06 Nov 2014, Accepted 07 Feb 2015, Published online: 23 Jun 2015

REFERENCES

  • J. Boussinesq, Theorie analytique de la chaleur, Gauthier-Villars, Paris, pp. 40–46, 1903.
  • R. E. Ewing, The Mathematics of Reservoir Simulation, Society for Industrial and Applied Mathematics, Philadelphia, pp. 35–106, 1983.
  • C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge University Press, Cambridge, UK, pp. 167–170, 1987.
  • Y. He, and J. Li, Numerical Comparisons of Time-Space Iterative Method and Spatial Iterative Methods for the Stationary Navier-Stokes Equations, J. Comput. Phys., vol. 231, pp. 6790–6800, 2012.
  • Y. He, Euler Implicit/Explicit Iterative Scheme for the Stationary Navier-Stokes Equations, Numeri. Math., vol. 123, pp. 67–96, 2013.
  • A. J. Chorin, Numerical Solution of the Navier-Stokes Equations, Math. Comput., vol. 22, pp. 745–762, 1968.
  • A. J. Chorin, On the Convergence of Discrete Approximations to the Navier-Stokes Equations, Math. Comput., vol. 23, pp. 341–353, 1969.
  • R. Temam, Sur l’approximation de la solution des equations de Navier-Stokes par la methode des fractionnarires II, Arch. Rational Mech. Anal., vol. 33, pp. 377–385, 1969.
  • H. Chen, J. Su, K. Li, and S. Wang, A Characteristic Projection Method for Incompressible Thermal Flow, Numer. Heat Transfer B., vol. 65, pp. 554–590, 2014.
  • C. Wu (1952). A General Theory of Three-Dimensional flow in Subsonic and Supersonic Turbomachines of axial-, radial-, and mixed-flow types, Lewis Flight Propulsion lab. Tech. rep. naca-tn-2604, Cleveland, Ohio.
  • K. Li, and A. Huang, The Navier-Strokes Equations in Stream Layer and on Stream Surface and a Dimension Split Methods, Acad. J. Xi’an Jiaotong Univ., vol. 14, pp. 89–101, 2002.
  • K. Li, A. Huang, and W. Zhang, A Dimension Split Method for the 3-D Compressible Navier-Stokes Equations in Turbomachine, Commun. Numer. Meth. Eng., vol. 18, pp. 1–14, 2002.
  • K. Li, W. Zhang, and A. Huang, An Asymptotic Analysis Method for the Linearly Shell Theory, Sci. China Ser. A, vol. 49, pp. 1009–1047, 2006.
  • H. Chen, K. Li, and S. Wang, A Dimension Split Method for the Incompressible Navier-Stokes Equations in Three Dimensions, Int. J. Numer. Meth. Fluids, vol. 73, pp. 409–435, 2013.
  • R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, 2nd ed.. Wiley, New York, pp. 75–103, 2001.
  • O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible flow, Gordon & Breach, New York, pp. 69–124, 1969.
  • J. L. Guermond, P. Minev, and J. Shen, An Overview of Projection Methods for Incompressible Flows, Comput. Meth. Appl. Mech. Eng., vol. 195, pp. 6011–6045, 2006.
  • Y. Hou, and H. Wei, Dimension Splitting Algorithm for a Three-Dimensional Elliptic Equation, Int. J. Comput. Math., vol. 89, pp. 112–127, 2012.
  • M. Hermanns Parallel Programming in Fortran 95 Using OpenMP, http://www.openmp.org/presentations/miguel/F95OpenMPv1v2.pdf, accessed on 19th April 2002.
  • U. Ghia, K. N. Ghia, and C. T. Shin, High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method, J. Comput. Phys., vol. 48, pp. 387–411, 1982.
  • O. Botella, and R. Peyret, Benchmark Spectral Results on the Lid-Driven Cavity Flow, Comput. Fluids, vol. 27, pp. 421–433, 1998.
  • R. Bouffanais, M. O. Deville, and E. Leriche, Large-Eddy Simulation of the Flow in a Lid-Driven Cubical Cavity, Phys. Fluids, vol. 19, pp. 55–108, 2007.
  • J. R. Koseff, and R. L. Street, The Lid-Driven Cavity Flow: A Synthesis of Qualitative and Quantitative Observations, J. Fluids Eng., vol. 106, pp. 390–398, 1984a.
  • J. R. Koseff, and R. L. Street, Visualization Studies of a Shear Driven Three-Dimensional Recirculating Flow, J. Fluids Eng., vol. 106, pp. 21–27, 1984b.
  • C. J. Freitas, R. L. Street, and A. N. Findikakis, and J. R. Koseff, Numerical Simulation of Three-Dimensional Flow in a Cavity, Int. J. Numer. Meth. Fluids, vol. 5, pp. 561–575, 1985.
  • C. J. Freitas, and R. L. Street, Non-Linear Transient Phenomena in a Complex Recirculating Flow: A Numerical Investigation, Int. J. Numer. Meth. Fluids, vol. 8, pp. 769–802, 1988.
  • V. Babu, and S. A. Korpela, Numerical Solution of the Incompressible Three-Dimensional Navier-Stokes Equations, Comput. Fluids, vol. 23, pp. 675–691, 1994.
  • C. Shu, X. D. Niu, and Y. T. Chew, Taylor Series Expansion and Least Squares-Based Lattice Boltzmann Method: Three-Dimensional Formulation and its Applications, Int. J. Mod. Phys. C, vol. 14, pp. 925–944, 2003.
  • R. W. Lewis, and K. Morgan, Numerical Method in Thermal Problem, Pineridge Press, Swansea, UK, pp. 338–348, 1979.
  • M. Hortmann, M. Peric, and G. Scheuerer, Finite Volume Multi Grid Prediction of Laminar Natural Convection: Benchmark Solutions, Int. J. Numer. Meth. Fluids, vol. 11, pp. 189–207, 1990.
  • N. Massarotti, P. Nithiarasu, and O. C. Zienkiewicz, Characteristic Based Split (CBS) Algorithm for Incompressible Flow Problems with Heat Transfer, Int. J. Numer. Meth. H., vol. 8, pp. 969–990, 1998.
  • B. Ramaswamy, T. C. Jue, and J. E. Akin, Semi-Implicit and Explicit Finite Element Schemes for Coupled Fluid/Thermal Problems, Int. J. Numer. Meth. Eng., vol. 34, pp. 675–696, 1992.
  • D. A. Mayne, A. S. Usmani, and M. Crapper, H-Adaptive Finite Element Solution of High Rayleigh Number Thermally Driven Cavity Problem, Int. J. Numer. Meth. H., vol. 10, pp. 598–615, 2000.
  • D. C. Lo, D. L. Young, K. Murugesan, C. C. Tsai, and M. H. Gou, Velocity-Vorticity Formulation for 3D Natural Convection in an Inclined Cavity by DQ Method, Int. J. Heat Mass Transfer, vol. 50, pp. 479–491, 2007.
  • E. Tric, G. Labrosse, and M. Betrouni, A First Incursion into the 3D Structure of Natural Convection of Air in a Differentially Heated Cubic Cavity, from Accurate Numerical Solutions, Int. J. Heat Mass Transfer, vol. 43, pp. 4043–4056, 2000.

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