An efficient SIMPLER-revised algorithm for incompressible flow with unstructured grids

References

• C. Geuzaine and J. F. Remacle, GMSH: A Three-Dimensional Finite Element Mesh Generator with Built-in Pre- and Post-processing Facilities, Int. J. Numer. Meth. Eng., vol. 79, no. 11, pp. 1309–1331, 2009.
   Web of Science ®Google Scholar
• S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington, DC, 1980.
   Google Scholar
• S. R. Mathur and J. Y. Murthy, A Pressure-Based Method for Unstructured Meshes, Numer. Heat Transfer B Fund., vol. 31, pp. 195–215, 1997.
   Web of Science ®Google Scholar
• S. Muzaferija, Adaptive Finite Volume Method for Flow Prediction Using Unstructured Meshes and Multi-Grid Approach, Ph.D. thesis, The University of London, London, pp.1–2, 1994.
   Google Scholar
• W. Q. Tao, Numerical Heat Transfer, 2nd ed., Xi’an Jiaotong University Press, Xi’an, 2001.
   Google Scholar
• J. D. Anderson Jr, Computational Fluid Dynamics. The Basics with Applications, McGraw-Hill Inc., New York, 1995.
   Google Scholar
• C. Taylor and P. Hood, A Numerical Solution of the Navier–Stokes Equations Using the Finite Element Technique. Comput. Fluids, vol. 1, pp. 73–100, 1973.
   Google Scholar
• D. K. Gartling, Finite Element Analysis of Viscous, Incompressible Fluid Flow, Ph.D. thesis, The University of Texas, Austin, Texas, 1975.
   Google Scholar
• L. Mangani, M. Darwish, and F. Moukalled, An OpenFOAM Pressure-Based Coupled CFD Solver for Turbulent and Compressible Flows in Turbomachinery Applications, Numer. Heat Transfer B Fund., pp. 1–19, 2016.
   Web of Science ®Google Scholar
• Z. Mazhar, A Novel Fully Implicit Block Coupled Solution Strategy for the Ultimate Treatment of the Velocity–Pressure Coupling Problem in Incompressible Fluid Flow, Numer. Heat Transfer B Fund., vol. 69, no. 2, pp. 130–149, 2016.
   Web of Science ®Google Scholar
• K. Luo, H. L. Yi, and H. P. Tan, Coupled Radiation and Mixed Convection in an Eccentric Annulus Using The Hybrid Strategy of Lattice Boltzmann-Meshless Method, Numer. Heat Transfer B Fund., vol. 66, pp. 243–267, 2014.
   Web of Science ®Google Scholar
• M. Darwish and F. Moukalled, A Fully Coupled Navier–Stokes Solver for Fluid Flow at All Speeds, Numer. Heat Transfer B Fund., vol. 65, no. 5, pp. 410–444, 2014.
   Web of Science ®Google Scholar
• M. E. Braaten, Development and Evaluation of Iterative and Direct Methods for the Solution of Equations Governing Recirculating Flows, Ph.D. thesis, The University of Minnesota, Minneapolis, MN, 1985.
   Google Scholar
• J. Kim and P. Moin, Application of a Fractional-Step Method to Incompressible Navier–Stokes Equations, J. Comput. Phys., vol. 59, pp. 308–323, 1985.
   Web of Science ®Google Scholar
• T. J. R. Hughes, W. K. Liu, and A. Brooks, Finite Element Analysis of Incompressible Viscous Flows by the Penalty Function Formulation. J. Comput. Phys., vol. 30, pp. 1–60, 1979.
   Web of Science ®Google Scholar
• M. E. Braaten and W. Shyy, Comparison of Iterative and Direct Method for Viscous Flow Calculations in Body-fitted Coordinates, Int. J. Numer. Meth. Fluids, vol. 6, pp. 325–349, 1986.
   Web of Science ®Google Scholar
• A. J. Chorin, A Numerical Method for Solving Incompressible Viscous Flow Problems, J. Comput. Phys., vol. 2, pp. 12–26, 1967.
   Google Scholar
• C. H. Sheng, D. L. Whitfield, and W. K. Anderson, A Multi-Block Approach for Calculating Incompressible Fluid Flows on Unstructured Grids, AIAA J., vol. 37, no. 2, pp. 169–176, 1999.
   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. 1787–1806, 1972.
   Web of Science ®Google Scholar
• B. Yu, H. Ozoe, and W. Q. Tao, A Modified Pressure-Correction scheme for the SIMPLER Method, MSIMPLER, Numer. Heat Transfer B Fund., vol. 39, pp. 439–449, 2001.
   Web of Science ®Google Scholar
• S. V. Patankar, A Calculation Procedure for Two-dimensional Elliptic Situations. Numer. Heat Transfer, vol. 4, pp. 409–425, 1981.
   Google Scholar
• J. P. van Doormaal and G. D. Raithby, Enhancement of the SIMPLE Method for Predicting Incompressible Fluid Flow. Numer. Heat Transfer, vol. 7, pp. 147–163, 1984.
   Google Scholar
• G. D. Raithby and G. E. Schneider, Elliptic System: Finite Difference Method II, in W. J. Minkowycz, E. M. Sparrow, R. H. Pletcher, and G. E. Schneider, (eds.), Handbook of Numerical Heat Transfer, pp. 241–289, Wiley, New York, 1988.
   Google Scholar
• R. I. Issa, Solution of Implicitly Discretized Fluid Flow Equation by Operator Splitting, J. Comput. Phys., vol. 62, pp. 40–65, 1985.
   Web of Science ®Google Scholar
• R. H. Yen and C. H. Liu, Enhancement of the SIMPLE Algorithm by an Additional Explicit Corrector Step, Numer. Heat Transfer B Fund., vol. 24, pp. 127–141, 1993.
   Web of Science ®Google Scholar
• W. Q. Tao, Z. G. Qu, and Y. L. He, A Novel Segregated Algorithm for Incompressible Fluid and Heat Transfer Problems-CLEAR (Coupled and Linked Equations Algorithm Revised) Part I: Mathematical Formulation and Solution Procedure, Numer. Heat Transfer B Fund., vol. 45, pp. 1–17, 2004.
   Web of Science ®Google Scholar
• D. L. Sun, W. Q. Tao, and Z. G. Qu, 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 Fund., vol. 53, pp. 1–17, 2007.
   Web of Science ®Google Scholar
• P. Ding and D. L. Sun, A Pressure-based Segregated Solver for Incompressible Flow on Unstructured Grids, Numer. Heat Transfer B Fund., vol. 64, no. 6, pp. 460–479, 2013.
   Web of Science ®Google Scholar
• S. C. Xue and G. W. Barton, A Finite Volume Formulation for Transient Convection and Diffusion Equations with Unstructured Distorted Grids and Its Applications in Fluid Flow Simulations with a Collocated Variable Arrangement, Comput. Meth. Appl. Mech. Eng., vol. 253, pp. 146–159, 2013.
   Web of Science ®Google Scholar
• M. Darwish and F. Moukalled, TVD Schemes for Unstructured Grids, Int. J. Heat Mass Transfer, vol. 46, no. 4, pp. 599–611, 2003.
   Web of Science ®Google Scholar
• L. X. Li, H. S. Liao, and L. J. Qi, An Improved r-Factor Algorithm for TVD Schemes, Int. J. Heat Mass Transfer, vol. 51, pp. 610–617, 2008.
   Web of Science ®Google Scholar
• J. Hou, F. Simons, and R. Hinkelmann, Improved TVD Schemes for Advection Simulation on Arbitrary Grids, Int. J. Numer. Meth. Fluids, vol. 70, pp. 359–382, 2012.
   Web of Science ®Google Scholar
• M. M. Athavale, Y. Jiang, and A. J. Przekwas, Application of an Unstructured Grid Solution Methodology to Turbomachinery Flows, AIAA Paper 98–0174, Reno, NV, 1995.
   Google Scholar
• P. K. Khosla and S. G. Rubin, A Diagonally Dominant Second-order Accurate Explicit Scheme, Comput. Fluid, vol. 2, pp. 207–209, 1974.
   Google Scholar
• P. J. Zeart and G. D. Raithby, An Integrated Space-time finite volume method for Moving-Boundary Problems, Numer. Heat Transfer B Fund., vol. 34, pp. 257–270, 1998.
   Web of Science ®Google Scholar
• P. Traore, Y. M. Ahopo, and C. Louste, A Robust and Efficient Finite Volume Scheme for the Discretization of Diffusive Flux on Extremely Skewed Meshes in Complex Geometries, J. Comput. Phys., vol. 228, pp. 5148–5159, 2009.
   Web of Science ®Google Scholar
• Y. Saad and M. H. Schultz, GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems, SIAM J. Sci. Stat. Comput., vol. 7, pp. 856–869, 1986.
   Web of Science ®Google Scholar
• C. M. Rhie and W. L. Chow, A Numerical Study of the Turbulent Flow Past an Isolated Airfoil with Trailing Edge Separation, AIAA J., vol. 21, pp. 1525–1535, 1983.
   Google Scholar
• S. Majumdar, Role of Underrelaxation in Momentum Interpolation for Calculation of Flow with Nonstaggered Grids, Numer. Heat Transfer, vol. 13, pp. 125–132, 1988.
   Web of Science ®Google Scholar
• S. K. Choi, Note on the Use of Momentum Interpolation Method for Unsteady Flows, Numer. Heat Transfer B Fund., vol. 36, pp. 545–550, 1999.
   Web of Science ®Google Scholar
• E. Blosch, W. Shyy, and R. Smith, The Role of Mass Conservation in Pressure-Based Algorithm, Numer. Heat Transfer B Fund., vol. 24, pp. 415–429, 1993.
   Web of Science ®Google Scholar
• U. Ghia, K. N. Ghia, and C. T. Shin, High-Re Solutions for Incompressible Flow Using the Navier–Stokes Equations and a Multi-Grid Method, J. Comput Phys., vol. 48, pp. 387–411, 1982.
   Web of Science ®Google Scholar
• E. Erturk, T. C. Corke, and C. Gokcol, Numerical Solutions of 2-D Steady Incompressible Driven Cavity Flow at High Reynolds Numbers. Int. J. Numer. Methods Fluids, vol. 48, no. 7, pp. 747–774, 2005.
   Web of Science ®Google Scholar