FIG. 2.

Equation (11) predicts the asymptotic behavior of Eq. (9) for a circular piston with radius a = 5λ. Here, the solid lines define the asymptotes indicated by Eq. (11) for n_l = 11 straight lines dividing the computational grid into n_s = 10 separate sectors. Two of the lines are coincident with the z and r axes, respectively, so only 9 straight lines are evident. The asymptotes are superposed over a contour plot of Eq. (9) evaluated for the same piston radius. The dashed lines show where 9 equally spaced contours are located in the same computational grid. The solid lines obtained from Eq. (11), which are easier to compute than the dashed contours, define an efficient grid sectoring scheme for pressure field calculations.