A formulation of Navier–Stokes problem in cylindrical coordinates applied to the 3D entry jet in a duct

A pseudospectral formulation of the three-dimensional Navier–Stokes equations in the cylindrical system of coordinates is presented, which automatically includes the regularity conditions at the polar axis for the Fourier harmonics. The mathematical system of equations is numerically implemented using standard methods for spatial discretisation and time advancement. The method presented here for incompressible flows can be easily extended to different set of equations and to different numerical schemes of various levels of accuracy. The formulation is applied to the solution of incompressible three-dimensional entry jets in a circular duct.