Table 1 Some tridimensional regularization functions [3]
From: The Full Non-linear Vortex Tube-Vorton Method: the pre-stall condition
Type | \({g}_{\sigma }\left(\overrightarrow{r}-{\overrightarrow{r}}_{v}\right)\) |
|---|---|
High order algebraic | \(\frac{{\rho }^{3}\left({\rho }^{2}+\frac{5}{2}\right)}{{\left({\rho }^{2}+1\right)}^{5/2}}\) |
2nd order Gaussian | \(1-{e}^{-{\rho }^{3}}\) |
Gaussian error function (erf) | \(\mathit{erf}\left(\frac{\rho }{\sqrt{2}}\right)-\rho \sqrt{\frac{2}{\pi }}{e}^{-\left(\frac{{\rho }^{2}}{2}\right)}\) |