Type II: Current-Centered Mesh

$$Z_{\rho^{+},i+\frac{1}{2},j} = Z_{\rho^{-},i+\frac{1}{2},j} = \frac{\Delta_{\rho}l_{\rho,i+\frac{1}{2},j}}{T}$$ (4.101)

$$Z_{\theta^{+},i,j+\frac{1}{2}} = Z_{\theta^{-},i,j+\frac{1}{2}} = \frac{\Delta_{\theta}l_{\theta,i,j+\frac{1}{2}}}{T}$$ (4.102)

$$Z_{c,i+\frac{1}{2},j} =$$ 0 (4.103)

$$Z_{c,i,j+\frac{1}{2}} =$$ 0 (4.104)

$$Y_{c,i,j} = \frac{2\Delta_{\rho}c_{u,i+\frac{1}{2},j}}{T}-\frac{T}{\Delta_{\r... ...{\rho}c_{u,i-\frac{1}{2},j}}{T}-\frac{T}{\Delta_{\rho}l_{\rho,i-\frac{1}{2},j}}$$

$$+ \frac{2\Delta_{\rho}c_{u,i,j+\frac{1}{2}}}{T}-\frac{T}{l_{\theta,... ...ac{2\Delta_{\rho}c_{u,i,j-\frac{1}{2}}}{T}-\frac{T}{l_{\theta,i,j-\frac{1}{2}}}$$

The stability bound is the same as given by (4.88), except that we take maxima over the series junction locations.

We leave out a discussion of the type III mesh because it was already shown in §4.4.2 to be relatively inefficient in terms of the maximum allowable time step for a given grid spacing (when compared to types I and II).