Development of Zonal-Embedded-Grid Method for a Polar Coordinate System and Application to the Spin-up Flow within a Semi-Circular Cylinder

A zonal embedded grid technique has been developed for computation of the two-dimensional Navier-Stokes equations with cylindrical coordinates. 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 spin-up flows within a semi-circular cylinder. It was shown that the numerical results were in good agreement with the experimental results both qualitatively and quantitatively.