Finite volume method with zonal-embedded grids for cylindrical coordinates

A zonal‐embedded‐grid technique has been developed for computation of the two‐dimensional Navier–Stokes equations with cylindrical coordinates. As is well known, the conventional regular grid system gives very small grid spacings in the azimuthal direction so it requires a very small time step for a stable numerical solution when the explicit method is used. The fundamental idea of the zonal‐embedded‐grid technique is that the number of azimuthal grids can be made small near the origin of the coordinates so that the grid size is more uniformly distributed over the domain than with the conventional regular‐grid system. The code developed using this technique combined with the explicit, finite‐volume method was then applied to calculation of the asymmetric swirl flows and Lamb's multi‐polar vortex flows within a full circle and the spin‐up flows within a semi‐circle. It was shown that the zonal‐embedded grids allow a time step far larger than the conventional regular grids. For the case of the Lamb's multi‐polar vortex flows, the code was validated by comparing the calculated results with the exact solutions. For the case of the semi‐circle spin‐up flows, the experimental results were used for the verification. It was seen that the numerical results were in good agreement with the experimental results both qualitatively and quantitatively. Copyright © 2006 John Wiley & Sons, Ltd.