A high-fidelity numerical method for the simulation of compressible flows in cylindrical geometries

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)