A novel efficient segregated pressure-based algorithm for steady-state incompressible flow

References

• A. Ashrafizadeh, B. Alinia and P. Mayeli, “A new co-located pressure-based discretization method for the numerical solution of incompressible Navier–Stokes equations,” Numer. Heat Transf. B: Fund., vol. 67, no. 6, pp. 563–589, 2015. DOI: https://doi.org/10.1080/10407790.2014.992094.
   Web of Science ®Google Scholar
• A. Ashrafizadeh and M. Nikfar, “On the numerical solution of generalized convection heat transfer problems via the method of proper closure equations – Part I: Description of the method,” Numer. Heat Transf. A: Appl., vol. 70, no. 2, pp. 187–203, 2016. DOI: https://doi.org/10.1080/10407782.2016.1173456.
   Web of Science ®Google Scholar
• P. Ding, “Solution of lid-driven cavity problems with an improved SIMPLE algorithm at high Reynolds numbers,” Int. J. Heat Mass Transfer., vol. 115, pp. 942–954, 2017. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2017.08.084.
   Web of Science ®Google Scholar
• H. Wang, H. Wang, F. Gao, P. Zhou and Z. J. Zhai, “Literature review on pressure–velocity decoupling algorithms applied to built-environment CFD simulation,” Build. Environ., vol. 143, pp. 671–678, 2018. DOI: https://doi.org/10.1016/j.buildenv.2018.07.046.
   Web of Science ®Google Scholar
• Z. J. Zhai, Computational Fluid Dynamics for Built and Natural Environments. Singapore: Springer, 2020.
   Google Scholar
• W. Q. Tao, Numerical Heat Transfer, 2nd ed. Xi’an: Xi’an Jiaotong University Press, 2001.
   Google Scholar
• I. Sezai, “Implementation of boundary conditions in pressure-based finite volume methods on unstructured grids,” Numer. Heat Transfer B: Fund., vol. 72, no. 1, pp. 82–107, 2017. DOI: https://doi.org/10.1080/10407790.2017.1338077.
   Web of Science ®Google Scholar
• F. Moukalled and M. Darwish, “A high resolution pressure-based algorithm for fluid flow at all speeds,” J. Comput. Phys., vol. 168, no. 1, pp. 101–133, 2001. DOI: https://doi.org/10.1006/jcph.2000.6683.
   Web of Science ®Google Scholar
• M. Darwish, I. Sraj, and F. Moukalled, “A coupled incompressible flow solver on structured grids,” Numer. Heat Transfer B: Fund., vol. 52, no. 4, pp. 353–371, 2007. DOI: https://doi.org/10.1080/10407790701372785.
   Web of Science ®Google Scholar
• L. Mangani, M. Buchmayr, and M. Darwish, “Development of a novel fully coupled solver in OpenFOAM: Steady-state incompressible turbulent flows,” Numer. Heat Transfer B: Fund., vol. 66, no. 1, pp. 1–20, 2014. DOI: https://doi.org/10.1080/10407790.2014.894448.
   Web of Science ®Google Scholar
• M. Darwish, A. A. Abdel, and F. Moukalled, “A coupled pressure-based finite-volume solver for incompressible two-phase flow,” Numer. Heat Transfer B: Fund., vol. 67, no. 1, pp. 47–74, 2015. DOI: https://doi.org/10.1080/10407790.2014.949500.
   Web of Science ®Google Scholar
• W. Q. Tao, Z. G. Qu, and Y. L. He, “A novel segregated algorithm for incompressible fluid flow 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, no. 1, pp. 1–17, 2004. DOI: https://doi.org/10.1080/1040779049025485.
   Web of Science ®Google Scholar
• T. Utnes, “A segregated implicit pressure projection method for incompressible flows,” J. Comput. Phys., vol. 227, no. 4, pp. 2198–2211, 2008. DOI: https://doi.org/10.1016/j.jcp.2007.11.022.
   Web of Science ®Google Scholar
• I. Sezai, “Transforming projection methods to solve steady incompressible flows,” Numer. Heat Transfer B: Fund., vol. 74, no. 2, pp. 538–558, 2018. DOI: https://doi.org/10.1080/10407790.2018.1525156.
   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. Methods Fluids, vol. 6, no. 6, pp. 325–349, 1986. DOI: https://doi.org/10.1002/fld.1650060603.
   Web of Science ®Google Scholar
• J. B. Bell, P. Colelia, and J. M. Glaz, “A second-order projection method for the incompressible Navier–Stokes equations,” J. Comput. Phys., vol. 85, no. 2, pp. 257–283, 1989. DOI: https://doi.org/10.1016/0021-9991(89)90151-4.
   Web of Science ®Google Scholar
• S. L. Lee and R. Y. Tzong, “Artificial pressure for pressure-linked equation,” Int. J. Heat Mass Transfer., vol. 35, no. 10, pp. 2705–2716, 1992. DOI: https://doi.org/10.1016/0017-9310(92)90111-5.
   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, no. 10, pp. 1787–1806, 1972. DOI: https://doi.org/10.1016/0017-9310(72)90054-3.
   Web of Science ®Google Scholar
• S. V. Patankar, “A calculation procedure for two-dimensional elliptic situations,” Numer. Heat Transfer., vol. 4, no. 4, pp. 409–425, 1981. DOI: https://doi.org/10.1080/01495728108961801.
   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. DOI: https://doi.org/10.1080/01495728408961817.
   Web of Science ®Google Scholar
• A. W. Date, “Numerical prediction of natural convection heat transfer in horizontal annulus,” Int. J. Heat Mass Transfer., vol. 29, no. 10, pp. 1457–1464, 1986. DOI: https://doi.org/10.1016/0017-9310(86)90060-8.
   Web of Science ®Google Scholar
• D. B. Spalding, “A general purpose computer program for multi-dimensional one-and two-phase flow,” Math. Comput. Simul., vol. 23, no. 3, pp. 267–276, 1981. DOI: https://doi.org/10.1016/0378-4754(81)90083-5.
   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: Fund., vol. 53, no. 1, pp. 1–17, 2008. DOI: https://doi.org/10.1080/10407790701632543.
   Web of Science ®Google Scholar
• D.-L. Sun, Z.-G. Qu, Y.-L. He, and W.-Q. Tao, “Performance analysis of IDEAL algorithm for three‐dimensional incompressible fluid flow and heat transfer problems,” Int. J. Numer. Meth. Fluids, vol. 61, no. 10, pp. 1132–1160, 2009. DOI: https://doi.org/10.1002/fld.2004.
   Web of Science ®Google Scholar
• D. L. Sun, Y. P. Yang, J. L. Xu, and W. Q. Tao, “Performance analysis of IDEAL algorithm combined with Bi-CGSTAB method,” Numer. Heat Transf. B: Fund., vol. 56, no. 6, pp. 411–431, 2010. DOI: https://doi.org/10.1080/10407790903526725.
   Web of Science ®Google Scholar
• D.-L. Son, W.-Q. Tao, J.-L. Xu and Z.-G. Qu, “Implementation of the IDEAL algorithm on nonorthogonal curvilinear coordinates for the solution of 3-D incompressible fluid flow and heat transfer problems,” Numer. Heat Transfer B: Fund., vol. 59, no. 2, pp. 147–168, 2011. DOI: https://doi.org/10.1080/10407790.2010.541357.
   Web of Science ®Google Scholar
• D. L. Sun, Q. P. Liu, J. L. Xu and W. Q. Tao, “Effects of inner iteration times on the performance of IDEAL algorithm,” Int. Commun. Heat Mass Transf., vol. 38, no. 9, pp. 1195–1200, 2011. DOI: https://doi.org/10.1016/j.icheatmasstransfer.2011.07.010.
   Web of Science ®Google Scholar
• D. Sun, S. Yu, B. Yu, P. Wang and W. Liu, “A VOSET method combined with IDEAL algorithm for 3D two-phase flows with large density and viscosity ratio,” Int. J. Heat Mass Transfer., vol. 114, pp. 155–168, 2017. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2017.06.050.
   Web of Science ®Google Scholar
• J. Li, Q. Zhang, and Z. J. Zhai, “An efficient SIMPLER-revised algorithm for incompressible flow with unstructured grids,” Numer. Heat Transfer B: Fund., vol. 71, no. 5, pp. 425–442, 2017. DOI: https://doi.org/10.1080/10407790.2017.1293965.
   Web of Science ®Google Scholar
• J. Li, Q. Zhang, and Z. J. Zhai, “An efficient segregated algorithm for two-dimensional incompressible fluid flow and heat transfer problems with unstructured grids,” Int. J. Heat Mass Transfer., vol. 133, pp. 1052–1064, 2019. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2018.12.039.
   Web of Science ®Google Scholar
• H. Xiao, J. Wang, Z. Liu and W. Liu, “A consistent SIMPLE algorithm with extra explicit prediction—SIMPLEPC,” Int. J. Heat Mass Transfer., vol. 120, pp. 1255–1265, 2018. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2017.12.119.
   Web of Science ®Google Scholar
• C. M. Rhie and W. L. Chow, “A numerical study of turbulent flow past an isolated airfoil with trailing edge separation,” AIAA J., vol. 21, no. 11, pp. 1525–1532, 1983. DOI: https://doi.org/10.2514/3.8284.
   Google Scholar
• 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, no. 3, pp. 387–411, 1982. DOI: https://doi.org/10.1016/0021-9991(82)90058-4.
   Web of Science ®Google Scholar
• E. Leriche and S. Gavrilakis, “Direct numerical simulation of the flow in a lid-driven cubical cavity,” Phys. Fluids, vol. 12, no. 6, pp. 1363–1376, 2000. DOI: https://doi.org/10.1063/1.870387.
   Web of Science ®Google Scholar
• D. Zhang, C. Jiang, D. Liang and L. Cheng, “A review on TVD schemes and a refined flux-limiter for steady-state calculations,” J. Comput. Phys., vol. 302, pp. 114–154, 2015. DOI: https://doi.org/10.1016/j.jcp.2015.08.042.
   Web of Science ®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, no. 7, pp. 953–967, 1990. DOI: https://doi.org/10.1002/fld.1650110704.
   Web of Science ®Google Scholar
• Y. Rouizi, Y. Favennec, J. Ventura and D. Petit, “Numerical model reduction of 2D steady incompressible laminar flows: application on the flow over a backward-facing step,” J. Comput. Phys., vol. 228, no. 6, pp. 2239–2255, 2009. DOI: https://doi.org/10.1016/j.jcp.2008.12.001.
   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. DOI: https://doi.org/10.1016/j.cma.2012.09.016.
   Web of Science ®Google Scholar
• G. Barakos, E. Mitsoulis, and D. O. Assimacopoulos, “Natural convection flow in a square cavity revisited: laminar and turbulent models with wall functions,” Int. J. Numer. Meth. Fluids, vol. 18, no. 7, pp. 695–719, 1994. DOI: https://doi.org/10.1002/fld.1650180705.
   Web of Science ®Google Scholar
• N. C. Markatos and K. A. Pericleous, “Laminar and turbulent natural convection in an enclosed cavity,” Int. J. Heat Mass Transfer, vol. 27, no. 5, pp. 755–772, 1984. DOI: https://doi.org/10.1016/0017-9310(84)90145-5.
   Web of Science ®Google Scholar
• P. Le Quéré, “Accurate solutions to the square thermally driven cavity at high Rayleigh number,” Comput. Fluids, vol. 20, no. 1, pp. 29–41, 1991. DOI: https://doi.org/10.1016/0045-7930(91)90025-D.
   Web of Science ®Google Scholar
• H. N. Dixit and V. Babu, “Simulation of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method,” Int. J. Heat Mass Transfer., vol. 49, nos. 3–4, pp. 727–739, 2006. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2005.07.046.
   Web of Science ®Google Scholar