Chu, P. and Fan, C., A three-point combined compact difference scheme, J. Comput. Phys. 140, 370–399 (1998).
 Chen, B.Y., He, D.D. and Pan, K.J., A linearized high-order combined compact difference scheme for multi-dimensional coupled Burgers’ equations, Numer. Math.-Theory. Me. In press.
 Denni, S.C.R. and Ng, M., Nguyen, P., Numerical solution for the steady motion of a viscous fluid inside a circular boundary using integral conditions, J. Comput. Phys. 108, 142–152 (1993).
 Ehrlich, L.W. and Gupta, M.M., Some difference schemes for the biharmonic equation, SIAM J. Numer. Anal. 12, 773–789 (1975).
 Greengard, L. and Kropinski, M.C., An integral equation approach to the incompressible Navier-Stokes equations in two dimensions, SIAM J. Sci. Comput. 20, 318–336 (1998).
 Gao, G.H. and Sun, H.W., Three-point combined compact alternating direction implicit difference schemes for two-dimensional time-fractional advection-diffusion equations, Commun. Comput. Phys. 17, 487–509 (2015).
 Gao, G.H. and Sun, H.W., Three-point combined compact difference schemes for time-fractional advection-diffusion equations with smooth solutions, J. Comput. Phys. 298, 520–538 (2015).
 He, D.D., An unconditionally stable spatial sixth-order CCD-ADI method for the two-dimensional linear telegraph equation, Numer. Algorithms 72, 1103–1117 (2016).
 He, D.D. and Pan, K.J., An unconditionally stable linearized CCD-ADI method for generalized nonlinear Schrödinger equations with variable coefficients in two and three dimensions, Comput. Math. Appl. 73, 2360–2374 (2017).
 Hanse, M.O.L. and Shen, W.Z., Vorticity-velocity formulation of the 3D Navier-Stokes equations in cylindrical co-ordinates, Int. J. Numer. Meth. Fl. 41, 29–45 (2003).
 Huang, W. and Tang, T., Pseudospectral solutions for steady motion of a viscous fluid inside a circular boundary, Appl. Numer. Math. 33, 167–173 (2000).
 Ito, K. and Qiao, Z.H., A high order compact MAC finite difference scheme for the Stokes equations: Augmented variable approach, J. Comput. Phys. 227, 8177–8190 (2008).
 Kohr, M. and Pop, I., Viscous incompressible flow for low Reynolds numbers, WIT, Southampton, Boston, 2004.
 Karageorghis, A. and Tang, T., A spectral domain decomposition approach for steady Navier-Stokes problems in circular geometries, Comput. Fluids 25, 541–549 (1996).
 Lai, M.C., A simple compact fourth-order poisson solver on polar geometry, J. Comput. Phys. 182, 337–345 (2002).
 Lai, M.C., Fourth-order finite difference scheme for the incompressible Navier-Stokes equations in a disk, Int. J. Numer. Meth. Fl. 42, 909–922 (2003).
 Lai, M.C., Lin, W.W. and Wang, W., A fast spectral/difference method without pole conditions for Poisson-type equations in cylindrical and spherical geometries, IMA J. Numer. Anal. 22, 537–548 (2002).
 Lai, M.C. and Liu, H.C., Fast direct solver for the biharmonic equation on a disk and its application to incompressible flows, Appl. Math. Comput. 164, 679–695 (2005).
 Lopez, J.M., Marques, F. and Shen, J., An efficient spectral-projection method for the Navier-Stokes equations in cylindrical geometries: II. three-dimensional cases, J. Comput. Phys. 176, 384–401 (2002).
 Lopez, J.M. and Shen, J., An efficient spectral-projection method for the Navier-Stokes equations in cylindrical geometries: I. axisymmetric cases, J. Comput. Phys. 139, 308–326 (1998).
 Lai, M.C. and Wang, W.C., Fast direct solvers for Poisson equation on 2D polar and spherical geometries, Numer. Meth. Part. D. E. 18, 56–68 (2002).
 Mahesh, K., A family of high order finite difference schemes with good spectral resolution, J. Comput. Phys. 145, 332–358 (1998).
 Mohseni, K. and Colonius, T., Numerical treatment of polar coordinate singularities, J. Comput. Phys. 157, 787–795 (2000).
 Nygård, F. and Andersson, H.I., On pragmatic parallelization of a serial Navier-Stokes solver in cylindrical coordinates, Int. J. Numer. Method. H. 22, 503–511 (2012).
 Nihei, T. and Ishii, K., A fast solver of the shallow water equations on a sphere using a combined compact difference scheme, J. Comput. Phys. 187, 639–659 (2003).
 Purcell, E.M., Life at low Reynolds number, Am. J. Phys. 45, 3–11 (1977).
 Pandit, S.K. and Karmakar, H., An efficient implicit compact streamfunction velocity formulation of two dimensional flows, J. Sci. Comput. 68, 653–688 (2016).
 Pulicani, J.P. and Ouazzani, J., A Fourier-Chebyshev pseudospectral method for solving steady 3-D Navier-Stokes and heat equations in cylindrical cavities, Comput. Fluids 20, 93–109 (1991).
 Sha, W., Nakabayashi, K. and Ueda, H., An accurate second-order approximation factorization method for time-dependent incompressible Navier-Stokes equations in spherical polar coordinates, J. Comput. Phys. 142, 47–66 (1998).
 Sun, H.W. and Li, L.Z., A CCD-ADI method for unsteady convection-diffusion equations, Comput. Phys. Commun. 185, 790–797 (2014).
 Lee, S.T., Liu, J. and Sun, H.W., Combined compact difference scheme for linear second-order partial differential equations with mixed derivative, J. Comput. Appl. Math. 264, 23–37 (2014).
 Sengupta, T.K., Lakshmanan, V. and Vijay, V., A new combined stable and dispersion relation preserving compact scheme for non-periodic problems, J. Comput. Phys. 228, 3048–3071 (2009).
 Sengupta, T.K., Vijay, V. and Bhaumik, S., Further improvement and analysis of CCD scheme: dissipation discretization and de-aliasing properties, J. Comput. Phys. 228, 6150–6168 (2009).
 Torres, D.J. and Coutsias, E.A., Pseudospectral solution of the two-dimensional Navier-Stokes equations in a disk, SIAM J. Sci. Comput. 21, 378–403 (1999).
 Tian, Z.F. and Yu, P.X., An efficient compact difference scheme for solving the streamfunction formulation of the incompressible Navier-Stokes equations, J. Comput. Phys. 230, 6404–6419 (2011).
 Verzicco, R. and Orlandi, P., A finite-difference scheme for three-dimensional incompressible flows in cylindrical coordinates, J. Comput. Phys. 123, 402–414 (1996).
 Yu, P.X. and Tian, Z.F., A compact scheme for the streamfunction-velocity formulation of the 2D steady incompressible Navier-Stokes equations in polar coordinaes, J. Sci. Comput. 56, 165–189 (2013).
 Zielinski, A.P., On trial functions applied in the generalized Trefftz method, Adv. Eng. Software 24, 147–155 (1995).