Transforming projection methods to solve steady incompressible flows

References

• 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
• S. V. Patankar, Numerical Heat Transfer and Fluid Flow. Washington D.C: Hemisphere Publishing Corporation, 1980.
   Google Scholar
• J. P. Van Doormaal, and G. D. Raithby, “Enhancements of the SIMPLE method for predicting incompressible fluid flows,” Numer Heat Transfer, vol. 7, no. 2, pp. 147–163, 1984.
   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 Part B, vol. 45, no. 1, pp. 1–17, 2004.
   Web of Science ®Google Scholar
• D. L. Sun, Z. G. Qu, Y. L. He, and W. Q. Tao, “An efficient seggregated algorithm for incompressible fluid flow and heat transfer Problems-IDEAL (InnerDoubly iterative efficient algorithm for linked equations), part I: Mathematical formulation and solution procedure,” Numer. Heat Transfer B, vol. 53, no. 1, pp. 1–17, 2008.
   Web of Science ®Google Scholar
• J. Li, Q. Zhang, and Z.-Q. Zhai, “An efficient SIMPLER-Revised algorithm for compressible flow with unstructured grids,” Numer. Heat Transfer B, vol. 71, no. 5, pp. 425–442, 2017.
   Web of Science ®Google Scholar
• R. Issa, A. D. Gosman, and A. P. Watkins, “The computation of compressible and incompressible recirculating flows by a non-iterative implicit scheme,” J. Comput. Phys., vol. 62, no. 1, pp. 66–82, 1986.
   Web of Science ®Google Scholar
• J. Kim, and P. Moin, “Application of fractional step method to incompressible Navier-Stokes equations,” Comput. Phys., vol. 59, no. 2, pp. 308–323, 1985.
   Google Scholar
• J. B. Bell, P. Colella, and H. M. Glaz, “A second-order projection method for the incompressible Navier-Stokes equations,” J. Comput. Phys., vol. 85, no. 2, pp. 257–283, 1989.
   Web of Science ®Google Scholar
• P. Gresho, “On the theory of Semi-Implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduce a nearly consistent mass matrix, part I: Theory,” Int. J. Numer. Methods Fluids, vol. 11, no. 5, pp. 587–620, 1990.
   Web of Science ®Google Scholar
• A. J. Chorin, “Numerical solution of Navier–Stokes equations,” Math. Comput., vol. 22, no. 104, pp. 745–742, 1968.
   Web of Science ®Google Scholar
• J. K. Dukowicz, and A. S. Dvinsky, “Approximation factorization as a high-order splitting for implicit incompressible flow equations,” J. Comput. Phys., vol. 102, no. 2, pp. 336–347, 1992.
   Web of Science ®Google Scholar
• J. B. Perot, “An analysis of the fractional step method,” J. Comput. Phys., vol. 108, no. 1, pp. 51–58, 1993.
   Web of Science ®Google Scholar
• H. Choi, and P. Moin, “Effects of the computational time step on numerical solutions of turbulent flow,” J. Comput. Phys., vol. 113, no. 1, pp. 1–4, 1994.
   Web of Science ®Google Scholar
• M.-J. Ni, and S. Komori, “General second-order projection formulas for unsteady flows,” AIAA J., vol. 40, no. 7, pp. 1464–1467, 2002.
   Google Scholar
• M. J. Ni, and M. A. Abdou, “A bridge between projection methods and SIMPLE type methods for incompressible Navier-Stokes equations,” Int. J. Numer. Methods Eng., vol. 72, no. 12, pp. 1490–1512, 2007.
   Web of Science ®Google Scholar
• I. Sezai, “Implementation of boundary conditions in pressure-based finite volume methods on unstructured grids,” Numer. Heat Transfer, Part B, vol. 72, no. 1, pp. 82–107, 2017.
   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, Part B, vol. 64, no. 6, pp. 460–479, 2013.
   Web of Science ®Google Scholar
• Q. Luo, T. Ren, and D. Liang, “Discretized pressure Poisson algorithm for the steady incompressible flow on a nonstaggered grid,” Numer. Heat Transfer, Part B, vol. 71, no. 6, pp. 549–559, 2017.
   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, no. 11, pp. 1525–1535, 1983.
   Google Scholar
• F. Denner, and B. G. M. van Wachem, “Fully-coupled balanced-force framework for arbitrary meshes with least-squares curvature evaluation from volume fractions,” Numerical Heat Transfer, Part B, vol. 65, no. 3, pp. 218–255, 2014.
   Web of Science ®Google Scholar
• P. Khosla, and S. Rubin, “A diagonally dominant second-order accurate implicit scheme,” Comput. Fluids, vol. 2, no. 2, pp. 207–209, 1974.
   Google Scholar
• Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd ed., Philadelphia: SIAM, 2003.
   Google Scholar
• 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
• L. Dailey, and R. Pletcher, “Evaluation of multigrid acceleration for preconditioned time-accurate Navier-Stokes algorithms,” Comput. Fluids, vol. 25, no. 8, pp. 791–811, 1996.
   Web of Science ®Google Scholar
• A. Dalal, V. Eswaran, and G. Biswas, “A finite-volume for Navier-Stokes equations on unstructured meshes,” Numer. Heat Transfer B, vol. 54, no. 3, pp. 238–259, 2008.
   Web of Science ®Google Scholar
• C. Lange, F. Durst, and M. Breuer, “Momentum and heat transfer from cylinders in laminar crossflow at 10−4 ≤ Re ≤200,” Int. J. Heat Mass Transfer, vol. 41, no. 22, pp. 3409–3430, 1998.
   Web of Science ®Google Scholar
• H.‐Q. Zhang, U. Fey, B. R. Noack, M. König, and H. Eckelmann, “On the transition of the cylinder wake,” Phys. Fluids, vol. 7, no. 4, pp. 779–794, 1995.
   Web of Science ®Google Scholar
• Z. Lilek, S. Muzaferija, M. Peric, and V. Seidl, “Computation of unsteady flows using nonmatching blocks of structured grid,” Numer. Heat Transfer B, vol. 32, no. 4, pp. 403–418, 1997.
   Web of Science ®Google Scholar
• M. Christon, P. Gresho, and S. Sutton, “Computational predictivity of time-dependent natural convection flows in enclosures including a benchmark solution,” Int. J. Numer. Meth. Fluids, vol. 40, no. 8, pp. 953–980, 2002.
   Web of Science ®Google Scholar