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PR summary
When calculating$\theta = 0$ or $\theta = \pi$ ,
vy
, whensinc=0
which causes division by 0. But the numerator should cancel due to azimuthal symmetry. So numerator is 0. So setvy=0
when that happens.Do it more precisely, expand out divergence in theta to be:$\frac{1}{r sin\theta} \frac{\partial (v sin\theta)}{\partial \theta}$ = $\frac{1}{r} \left(\frac{\Delta v}{\Delta \theta} + v cot\theta \right)$ . Both $\Delta v = 0$ and $v = 0$ at $\theta = 0$ , so we have $\frac{1}{r} \frac{cos \theta v}{sin \theta} = 0/0$ . With l'hopital, we have $lim_{\theta \rightarrow 0} \frac{\partial(v cos \theta) / \partial \theta}{cos \theta } = 0$
PR motivation
PR checklist
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file has been updated, if appropriate