An axis treatment for flow equations in cylindrical coordinates based on parity conditions

A novel axis treatment using parity conditions is presented for flow equations in cylindrical coordinates that are represented in azimuthal Fourier modes. The correct parity states of scalars and the velocity vector are derived such that symmetry conditions for each Fourier mode of the respective variable can be determined. These symmetries are then used to construct finite-difference and filter stencils at and near the axis, and an interpolation scheme for the computation of terms premultiplied by 1/r. A grid convergence study demonstrates that the axis treatment retains the formal accuracy of the spatial discretization scheme employed. Two further test cases are considered for evaluation of the axis treatment, the propagation of an acoustic pulse and direct numerical simulation of a fully turbulent supersonic axisymmetric wake. The results demonstrate the applicability of the axis treatment for non-axisymmetric flows.