Approximate factorization of the discrete Navier–Stokes equations in Cartesian and cylindrical coordinates

A new pseudospectral technique for integrating incompressible Navier–Stokes equations with one nonperiodic boundary in Cartesian or cylindrical coordinate system is presented. Algorithm constructed makes use of Chebyshev collocation technique in nonperiodic direction. Special attention is paid to the approximate factorization of the discrete Navier–Stokes equations in cylindrical geometry leading to highly fast and robust numerical procedure providing spectral accuracy. New approach is an efficient tool for further investigation of turbulent shear flows, for physical hypotheses and alternative algorithms testing. Classical problems of incompressible fluid flows in an infinite plane channel and annuli at transitional Reynolds numbers are taken as model ones.