A New Co-Located Pressure-Based Discretization Method for the Numerical Solution of Incompressible Navier-Stokes Equations

REFERENCES

• M. Darwish, I. Sraj, and F. Moukalled A Coupled Incompressible Flow Solver on Structured Grids, Numer. Heat Transfer B, vol. 52, pp. 353–371, 2007.
   Web of Science ®Google Scholar
• C. F. Kettleborough, S. R. Husain, and C. Prakash Solution of Fluid Flow Problems with the Vorticity-Stream Function Formulation, and the Control-Volume-Based Finite Element Method, Numer. Heat Transfer B, vol. 16, pp. 31–58, 1990.
   Web of Science ®Google Scholar
• G. Comini, G. Cortella, and M. Manzan A Stream Function-Vorticity-Based Finite-Element Formulation for Laminar-Convection Problems, Numer. Heat Transfer B, vol. 28, pp. 1–22, 1995.
   Web of Science ®Google Scholar
• E. Erturk, T. C. Corke, and C. Gökçöl Numerical Solutions of 2-D Steady Incompressible Driven Cavity Flow at High Reynolds Numbers, Int. J. Numeri. Meth. Fluids, vol. 48, pp. 747–774, 2005.
   Web of Science ®Google Scholar
• H. Ozoe, K. Fujii, T. Shibata, H. Kuriyama, and S. W. Churchill Three-Dimensional Numerical Analysis of Natural Convection in a Spherical Annulus, Numer. Heat Transfer B, vol. 8, pp. 383–406, 1985.
   Web of Science ®Google Scholar
• V. Bubnovich, C. Rosas, R. Santander, and G. Cáceres Computation of Transient Natural Convection in a Square Cavity by an Implicit Finite-Difference Scheme in Terms of the Stream Function, and Temperature, Numer. Heat Transfer A, vol. 42, pp. 401–425, 2002.
   Web of Science ®Google Scholar
• A. J. Chorin Numerical Solution of Navier-Stokes Equations, Math. Comput., vol. 22, pp. 745–762, 1968.
   Web of Science ®Google Scholar
• T. M. Shih, C. H. Tan, and B. C. Hwang Equivalence of Artificial Compressibility Method, and Penalty-Function Method, Numer. Heat Transfer B, vol. 15, pp. 127–130, 1989.
   Web of Science ®Google Scholar
• T. S. Lee, L. Wei, and H. T. Low Development of an Artificial Compressibility Methodology with Implicit LU-SGS Method, Int. J. Comput. Fluid Dynam., vol. 15, pp. 197–208, 2001.
   Web of Science ®Google Scholar
• D. Pan, Y. S. Yang, and C. H. Chang Computation of Internal Flow with Free Surfaces Using Artificial Compressibility, Numer. Heat Transfer B, vol. 42, pp. 401–425, 2002.
   Google Scholar
• S. V. Patankar, and D. B. Spalding A Caculation Procedure for Heat, Mass and Momentum Transfer in 3-D 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, Numer. Heat Transfer B, vol. 53, pp. 1–17, 2008.
   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, Phys. 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. Comput. Phys, 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 J., vol. 21, pp. 1525–1532, 1983.
   Google Scholar
• M. Peric Analysis of Pressure-Velocity Coupling on Non-orthogonal Grids, Numer. Heat Transfer B, vol. 17, pp. 63–82, 1990.
   Web of Science ®Google Scholar
• F. S. Lien A Pressure-Based Unstructured Grid Method for All Speed Flows, Int. J. Numer. Meth. Fluids, vol. 33, pp. 355–374, 2000.
   Web of Science ®Google Scholar
• J. Papageorgakopoulos, G. Arampatzis, D. Assimacopoulos, and N. C. Markatos Enhancement of the Momentum Interpolation Method on Non-staggered Grids, Int. J. Numer. Meth. Fluids, vol. 33, pp. 1–22, 2000.
   Web of Science ®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
• A. Ashrafizadeh, M. Rezvani, and B. Bakhtiari Pressure-Velocity Coupling on Co-located Grids Using the Method of Proper Closure Equations, Numer. Heat Transfer B, vol. 56, pp. 259–273, 2009.
   Web of Science ®Google Scholar
• P. M. Gresho and R. L. Sani On Pressure Boundary Conditions for the Incompressible Navier‐Stokes Equations, Int. J. Numer. Meth. Fluids, vol. 7, pp. 1111–1145, 1987.
   Web of Science ®Google Scholar
• E. Erturk Discussions on Driven Cavity Flow, Int. J. Numer. Meth. Fluids, vol. 60, pp. 275–294, 2009.
   Web of Science ®Google Scholar
• E. M. Wahba Steady Flow Simulations inside a Driven Cavity up to Reynolds Number 35,000, Comput. Fluids, vol. 66, pp. 85–97, 2012.
   Web of Science ®Google Scholar
• K. Yapici and Y. Uludag Finite Volume Simulation of 2-D Steady Square Lid Driven Cavity Flow at High Reynolds Numbers, Brazil. J. Chemi. Eng, vol. 30, pp. 923–927, 2013.
   Web of Science ®Google Scholar
• I. G. Currie Fundamental Mechanics of Fluids, McGraw-Hill, New York, 1974.
   Google Scholar
• D. K. Gartling A Test Problem for Outflow Boundary Conditions–Flow over a Backward Facing Step, Int. J. Numer. Meth. Fluids, vol. 11, pp. 953–969, 1990.
   Web of Science ®Google Scholar
• E. Erturk Numerical Solutions of 2-D Steady Incompressible Flow over a Backward Facing Step Part I: High Reynolds Number Solutions, J. Compu. Fluids, vol. 37, pp. 633–655, 2008.
   Web of Science ®Google Scholar