Running summarizing tools on a new article

Abstract: Abstract A wide range of flows of practical interest occur in cylindrical geometries. In order to simulate such flows, an available compact finite‐difference simulation code [1] was adapted by introducing a mapping that expresses cylindrical coordinates as generalized coordinates. This formulation is conservative and avoids problems associated with the classical formulation of the Navier‐Stokes equations in cylindrical coordinates. The coordinate singularity treatment follows [2] and is modified for generalized coordinates. To retain high‐order numerical accuracy, a Fourier spectral method is employed in the azimuthal direction combined with mode clipping to alleviate time‐step restrictions due to a very fine grid spacing near the singularity at the axis (r = 0). An implementation of this scheme was successfully validated by a simulation of a tripolar vortex formation and by comparison with linear stability theory. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)