A finite difference method for 3D incompressible flows in cylindrical coordinates

In this work, a finite difference method to solve the incompressible Navier–Stokes equations in cylindrical geometries is presented. It is based upon the use of mimetic discrete first-order operators (divergence, gradient, curl), i.e. operators which satisfy in a discrete sense most of the usual properties of vector analysis in the continuum case. In particular the discrete divergence and gradient operators are negative adjoint with respect to suitable inner products. The axis r = 0 is dealt with within this framework and is therefore no longer considered as a singularity. Results concerning the stability with respect to 3D perturbations of steady axisymmetric flows in cylindrical cavities with one rotating lid, are presented.