Fourth-order central compact scheme for the numerical solution of incompressible Navier–Stokes equations

References

• B.F. Armaly, F. Durst, J.C.F. Pereira, and B. Schonung, Experimental and theoretical investigation of backward facing step flow, J. Fluid Mech. 172 (1983), pp. 473–496. doi: 10.1017/S0022112083002839
   Web of Science ®Google Scholar
• R. Beam and R.F. Warming, An implicit scheme for the compressible Navier–Stokes equations, AIAA J. 16 (2005), pp. 393–402. doi: 10.2514/3.60901
   Google Scholar
• M.H. Carpenter, D. Gottlieb, and S. Abarbanel, The stability of numerical boundary treatments for compact high-order finite-difference schemes, J. Comput. Phys. 108 (1993), pp. 272–295. doi: 10.1006/jcph.1993.1182
   Web of Science ®Google Scholar
• A.J. Chorin, A numerical method for solving incompressible viscous flow problems, J. Comput. Phys. 2 (1967), pp. 12–26. doi: 10.1016/0021-9991(67)90037-X
   Google Scholar
• D. Drikakis and W. Rider, High-Resolution Methods for Incompressible and Low-Speed Flows, Springer, Berlin, 2005.
   Google Scholar
• J.A. Ekaterinaris, High-order accurate numerical solutions of incompressible flows with the artificial compressible method, Int. J. Numer. Meth. Fluids 45 (2004), pp. 1187–1207. doi: 10.1002/fld.727
   Web of Science ®Google Scholar
• D.V. Gaitonde and M.R. Visbal, Further development of a Navier–Stokes solution procedure based on higher-order formulas, AIAA paper 1999–0557, 1999.
   Google Scholar
• D.V. Gaitonde and M.R. Visbal, On the use of higher-order finite-difference schemes on curvilinear and deforming meshes, J. Comput. Phys. 181 (2002), pp. 155–185. doi: 10.1006/jcph.2002.7117
   Web of Science ®Google Scholar
• D.K. Gartling, A test problem for outflow boundary conditions, flow over a backward facing step, Int. J. Numer Methods Fluids 11 (1990), pp. 953–967. doi: 10.1002/fld.1650110704
   Web of Science ®Google Scholar
• A. Jameson, Time dependent calculation using multigrid with application to unsteady flows past airfoils and wings, AIAA paper, 1991, 1591–1596.
   Google Scholar
• J. Kim and P. Moin, Application of a fractional step method to incompressible Navier–Stokes equations, J. Comput. Phys. 59 (1985), pp. 308–323. doi: 10.1016/0021-9991(85)90148-2
   Web of Science ®Google Scholar
• L.I.G. Kovasznay, Laminar flow behind a two dimensional grid, Proc. Camb. Philos. 44 (1948), pp. 58–62. doi: 10.1017/S0305004100023999
   Web of Science ®Google Scholar
• D. Kwak and S.R. Chakravarthy, A three dimensional incompressible Navier–Stokes flow solver using primitive variables, AIAA J. 24(2) (1986), pp. 390–396. doi: 10.2514/3.9279
   Google Scholar
• S.K. Lele, Compact finite difference schemes with spectral-like resolution, Journal of Comput. Phys. 103 (1992), pp. 16–42. doi: 10.1016/0021-9991(92)90324-R
   Web of Science ®Google Scholar
• X. Liang, X.L. Li, D.X. Fu, and Y.W. Ma, Complex transition of double diffusive convection in a rectangular enclosure with height to length ratio equal to 4: part I, Commun. Comput. Phys. 6 (2) (2009), pp. 247–268. doi: 10.4208/cicp.2009.v6.p247
   Web of Science ®Google Scholar
• V. Prabhakar and J.N. Reddy, Spectral/hp penality least-square finite element formulation for the steady incompressible Navier–Stokes equations, J. Comput. Phys. 215 (2006), pp. 274–297. doi: 10.1016/j.jcp.2005.10.033
   Web of Science ®Google Scholar
• Q. Qin, Z.A. Xia, and Z.F. Tian, High accuracy numerical investigation of double diffusive convection in a rectangular enclosure with horizontal temperature and concentration gradients, Int. J. Heat Mass Transfer 71 (2014), pp. 405–423. doi: 10.1016/j.ijheatmasstransfer.2013.12.035
   Web of Science ®Google Scholar
• M. Rizwan, A. Shah, and L. Yuan, A central compact scheme for numerical solution of two-phase incompressible flow using Allen-Cahn phase-field model, J. Braz. Soc. Mech. Sci. Eng. 38 (2016), pp. 433–441. doi: 10.1007/s40430-015-0342-4
   Web of Science ®Google Scholar
• S.E. Rogers and D. Kwak, An upwind differencing scheme for the time accurate incompressible Navier–Stoke equations, AIAA J. 28(2) (1990), pp. 253–262. doi: 10.2514/3.10382
   Google Scholar
• S.E. Rogers and D. Kwak, An upwind differencing scheme for the incompressible Navier–Stokes equations, Appl. Numer. Math. 1 (8) (1991), pp. 43–64. doi: 10.1016/0168-9274(91)90097-J
   Web of Science ®Google Scholar
• A. Shah and L. Yuan, Flux-difference splitting based upwind compact scheme for the incompressible Navier-Stokes equations, Int. J. Numer. Meth. Fluids 61 (2009), pp. 552–568. doi: 10.1002/fld.1965
   Web of Science ®Google Scholar
• A. Shah and L. Yuan, Upwind compact finite difference scheme for time-dependent Incompressible Navier-Stokes Equations, Appl. Math. Comput. 215 (2010), pp. 3201–3213.
   Web of Science ®Google Scholar
• Z.F. Tian, X. Liang, and P.X. Yu, A higher order compact finite difference algorithm for solving the incompressible Navier Stokes equations, Int. J. Numer. Methods Eng. 88 (2011), pp. 511–532. doi: 10.1002/nme.3184
   Web of Science ®Google Scholar
• J.B. Zhang and Z.S. Qian, Implicit eighth-order central compact scheme for the numerical simulation of steady and unsteady incompressible Navier-Stokes equations, Int. J. Comput. Fluid Dyn. 26 (2012), pp. 247–261. doi: 10.1080/10618562.2012.690511
   Web of Science ®Google Scholar