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![$\displaystyle Y_{\rho^{+},i,j} = Y_{\rho^{-},i,j} = Y_{\theta^{+},i,j} = Y_{\theta^{-},i,j} = \frac{\Delta_{\rho}c_{u,i,j}}{2T}\hspace{0.3in}Y_{c,i,j} = 0$](img1826.png) |
(4.97) |
The stability constraints (which follow from the requirement of positivity of
everywhere) are
![$\displaystyle \frac{\Delta_{\rho}}{T}\geq \max_{i,j}\sqrt{\frac{2}{l_{i,j}c_{i,...
...{T}\geq\max_{i,j}\left(\frac{1}{\rho_{i}}\sqrt{\frac{2}{l_{i,j}c_{i,j}}}\right)$](img1829.png) |
(4.100) |
There is thus a dependence on
in the second condition (relating the angular spacing
to
), which we expect, since the spacing between the junctions at a given radius now varies linearly with the radius. Stability bounds are, for a radial mesh, necessarily more severe than in the rectilinear case, due to this variation in grid spacing.
Stefan Bilbao
2002-01-22