On the numerical solution of generalized convection heat transfer problems via the method of proper closure equations – part I: Description of the method

References

• T. L. Bergman, A. S. Lavine, F. P. Incropera, and D. P. Dewit, Fundamentals of Heat and Mass Transfer, John Wiley & Sons, New York, 2011.
   Google Scholar
• J. H. Ferziger, and M. Peric, Computational Methods for Fluid Dynamics, Springer, New York, 2002.
   Google Scholar
• H. Versteeg, and W. Malalasekera, An Introduction to Computational Fluid Dynamics, Pearson, London, 2007.
   Google Scholar
• S. Acharya, B. R. Baliga, K. Karki, J. Y. Murthy, C. Prakash, and S. P. Vanka, Pressure-Based Finite-Volume Methods in Computational Fluid Dynamics, J. Heat Transfer, vol. 129, pp. 407–424, 2007.
   Web of Science ®Google Scholar
• F. H. Harlow and J. E. Welch, Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid With Free Surface, Physics of Fluids, vol. 8, pp. 2182–2189, 1965.
   Web of Science ®Google Scholar
• C. W. Hirt, A. A. Amsden, and L. Cook, An Arbitrary Lagrangian Eulerian Computing Method for All Flow Speed, J. Computational Physics, vol. 14, pp. 227–253, 1974.
   Web of Science ®Google Scholar
• C. M. Rhie, and W. L. Chow, Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation, AIAA Journal vol. 21, pp. 1525–1532, 1983.
   Web of Science ®Google Scholar
• E. Chenier, R. Eymard, and R. Herbin, A Collocated Finite Volume Scheme to Solve Free Convection for General Non-Conforming Grids, J. Computational Physics, vol. 228, pp. 2296–2311, 2009.
   Web of Science ®Google Scholar
• R. Abbasi, A. Ashrafizadeh, and A. Shadaram, A Comparative Study of Finite Volume Pressure-Correction Projection Methods on Co-located Grid Arrangements, Computers and Fluids, vol. 81 pp. 68–84, 2013.
   Web of Science ®Google Scholar
• D. Pan, A High-Order Piecewise Polynomial Reconstruction for Finite-Volume Methods Solving Convection and Diffusion Equations, Numerical Heat Transfer Part B, vol. 68, pp. 495–510, 2015.
   Web of Science ®Google Scholar
• A. Ashrafizadeh, B. A. Bavafa, and P. Mayeli, A New Co-located Pressure-Based Discretization Method for the Numerical Solution of Incompressible Navier-Stokes Equations, Numerical Heat Transfer Part B, vol. 67, pp. 563–589, 2015.
   Web of Science ®Google Scholar
• A. Ashrafizadeh, M. Rezvani, and B. Bakhtiari, Pressure-Velocity Coupling on Co-located Grids Using the Method of Proper Closure Equations, Numerical Heat Transfer Part B, vol. 56, pp. 259–273, 2009.
   Web of Science ®Google Scholar
• M. Rezvani and A. Ashrafizadeh, Numerical Simulation of the Inter-Equation Couplings in All-Speed Flows via the Method of Proper Closure Equations, Numerical Heat Transfer part A, vol. 58, pp. 313–332, 2010.
   Web of Science ®Google Scholar
• P. F. Galpin and G. D. Raithby, Numerical Solution of Problems in Incompressible Fluid Flow: Treatment of the Temperature-Velocity Coupling, Numerical heat transfer, vol. 10, pp. 105–129, 1986.
   Web of Science ®Google Scholar
• S. V. Patankar and D. B. Spalding, A Calculation Procedure for Heat Mass and Momentum Transfer in Three-Dimensional Parabolic Flows, Int. J. Heat Mass Transfer, vol. 15, pp. 1767–1806, 1972.
   Web of Science ®Google Scholar
• D. L. Sun, Z. G. Qu, Y. L. He, and W. Q. Tao, An Efficient Segregated Algorithm for Incompressible Fluid Flow and Heat Transfer Problems-IDEAL (Inner Doubly Iterative Efficient Algorithm for Linked Equations) Part I: Mathematical formulation and solution procedure, Numerical heat transfer Part B, vol. 53, pp. 1–17, 2008.
   Web of Science ®Google Scholar
• P. F. Galpin, and G. D. Raithby, Treatment of Non-Linearities in the Numerical Solution of the Incompressible Navier-Stokes Equations, Int. J. Numerical Methods in Fluids vol. 6, pp. 409–426, 1986.
   Web of Science ®Google Scholar
• Z. Mazhar, A Procedure for the Treatment of the Velocity-Pressure Coupling Problem in Incompressible Fluid Flow, Numerical Heat Transfer Part B, vol. 39, pp. 91–100, 2001.
   Web of Science ®Google Scholar
• N. Chidambaram, and R. Pletcher, A Collocated-Grid, Fully Coupled Algorithm for Large Eddy Simulation of Incompressible and Compressible Flows, Numerical Heat Transfer Part B, vol. 37 1–23, 2000.
   Web of Science ®Google Scholar
• T. W. H. Sheu and R. K. Lin, Newton Linearization of the Incompressible Navier-Stokes Equations, Int. J. Numerical Methods in Fluids, vol. 44, pp. 297–312, 2004.
   Web of Science ®Google Scholar
• M. Darwish, I. Sraj, and F. Moukalled, A Coupled Incompressible Flow Solver on Structured Grid, Numerical Heat Transfer Part B, vol. 52, pp. 353–371, 2007.
   Web of Science ®Google Scholar
• A. Cubero and N. Fueyo, Preconditioning Based on a Partially Implicit Implementation of Momentum Interpolation for Coupled Solvers, Numerical Heat Transfer Part B, vol. 53, pp. 510–535, 2008.
   Web of Science ®Google Scholar
• M. Darwish and I. S. F. Moukalled, A Coupled Finite Volume Solver for the Solution of Incompressible Flows on Unstructured Grids, J. Computational Physics, vol. 228, pp. 180–201, 2009.
   Web of Science ®Google Scholar
• Z. J. Chen and A. J. Przekwas, A Coupled Pressure-Based Computational Method for Incompressible/Compressible Flows, J. Computational Physics, vol. 229, pp. 9150–9165, 2010.
   Web of Science ®Google Scholar
• M. Darwish and I. S. F. Moukalled, A Fully Coupled Navier-Stokes Solver for Fluid Flow at all Speeds, Numerical Heat Transfer Part B, vol. 45, pp. 410–444, 2014.
   Web of Science ®Google Scholar
• B. R. Hutchinson, P. F. Galpin, and G. D. Raithby, Application of Additive Correction Multigrid to the Coupled Fluid-Flow Equations, Numerical Heat Transfer, vol. 13, pp. 133–147, 1988.
   Web of Science ®Google Scholar
• L. Davidson, 2nd-Order Corrections of the k-ε Model to Account for Nonisotropic Effects Due to Buoyancy, Int. J. Heat and Mass Transfer, vol. 33, pp. 2599–2608, 1990.
   Web of Science ®Google Scholar
• P. R. McHugh and D. A. Knoll, Fully Coupled Finite-Volume Solutions of the Incompressible Navier-Stokes and Energy Equations Using an Inexact Newton Method, Int. J. Numerical Methods in Fluids, vol. 19, pp. 439–455, 1994.
   Web of Science ®Google Scholar
• R. W. Johnson, P. R. McHugh, D. A. Knoll, Defect Correction with a Fully Coupled Inexact Newton Method, Numerical Heat Transfer Part B, vol. 26, pp. 173–188, 1994.
   Web of Science ®Google Scholar
• S. Vakilipour and S. J. Ormiston, A Coupled Pressure-Based Co-Located Finite-Volume Solution Method for Natural-Convection Flows, Numerical Heat Transfer Part B, vol. 61, pp. 91–115, 2012.
   Web of Science ®Google Scholar
• A. Bejan, Convection Heat Transfer, John Wiley & Sons, New York, 2004.
   Google Scholar
• G. E. Schneider, and M. J. Raw, Control Volume Finite-Element Method for Heat Transfer and Fluid Flow Using Collocated Variables 1- Computational Procedure, Numerical Heat Transfer vol. 11, pp. 363–390, 1987.
   Web of Science ®Google Scholar
• A. Ashrafizadeh, G.D. Raithby, and G.D. Stubley, Direct Design of Ducts, J. Fluids Engineering vol. 125, pp. 158–165, 2003.
   Web of Science ®Google Scholar