[en] The scaling law for the $m/n=3/2$ error field (EF) penetration threshold is predicted numerically based on non-linear single-fluid and two-fluid modeling using the TM1 code. The simulated penetration threshold of radial magnetic field b _r at the plasma edge is scaled to the electron density n _e, temperature T _e, viscous time ${\mathrm{\tau <!--\; ??\; -->}}_{\mathrm{\mu <!--\; ??\; -->}}$, toroidal field B _t and the natural frequency ω in the form of $b_r/B_t\propto <!--\; ???\; -->n_e^{{\mathrm{\alpha <!--\; ??\; -->}}_n}{T}_e^{{\mathrm{\alpha <!--\; ??\; -->}}_T}{\mathrm{\tau <!--\; ??\; -->}}_{\mathrm{\mu <!--\; ??\; -->}}^{{\mathrm{\alpha <!--\; ??\; -->}}_{\mathrm{\mu <!--\; ??\; -->}}}{B}_t^{{\mathrm{\alpha <!--\; ??\; -->}}_B}{\mathrm{\omega <!--\; ??\; -->}}^{{\mathrm{\alpha <!--\; ??\; -->}}_{\mathrm{\omega <!--\; ??\; -->}}}$ by scanning these parameters separately. Here, α _n, α _T, ${\mathrm{\alpha <!--\; ??\; -->}}_{\mathrm{\mu <!--\; ??\; -->}}$, α _B and ${\mathrm{\alpha <!--\; ??\; -->}}_{\mathrm{\omega <!--\; ??\; -->}}$ are the scaling coefficients on n _e, T _e, ${\mathrm{\tau <!--\; ??\; -->}}_{\mathrm{\mu <!--\; ??\; -->}}$, B _t and ω, respectively. Single-fluid modeling shows that the 3/2 EF threshold scales as $b_r/B_t\propto <!--\; ???\; -->n_e^{0.56}{T}_e^{0.6}{\mathrm{\tau <!--\; ??\; -->}}_{\mathrm{\mu <!--\; ??\; -->}}^{-<!--\; ???\; -->0.59}{B}_t^{-<!--\; ???\; -->1.15}\mathrm{\omega <!--\; ??\; -->}$, which is similar with the analytical scaling law in both the Rutherford and visco-resistive regimes. However, two-fluid modeling shows that the scaling law differs significantly in particular regarding the dependence on plasma rotation. In detail, the scaling coefficient α _n on density decreases from 0.67 to 0.56 and α _T on temperature decreases from 0.67 to 0.32, while ${\mathrm{\alpha <!--\; ??\; -->}}_{\mathrm{\mu <!--\; ??\; -->}}$ on viscous time is around -0.45 and α _B on toroidal field decreases slightly from -1.15 to -1, when the ratio $|{\mathrm{\omega <!--\; ??\; -->}}_E/{\mathrm{\omega <!--\; ??\; -->}}_{\ast <!--\; ???\; -->e}|$ between plasma rotation frequency ω _E and diamagnetic drift frequency ω _*e varies from 0 to 10. Scans of the plasma rotation reveals that the penetration threshold linearly depends on the perpendicular electron flow frequency (or natural frequency) ${\mathrm{\omega <!--\; ??\; -->}}_{\perp <!--\; ???\; -->e}={\mathrm{\omega <!--\; ??\; -->}}_E+{\mathrm{\omega <!--\; ??\; -->}}_{\ast <!--\; ???\; -->e}$, and there is a minimum in the required field amplitude when ${\mathrm{\omega <!--\; ??\; -->}}_{\perp <!--\; ???\; -->e}\sim <!--\; ???\; -->0$. In addition, the enduring mystery of non-zero penetration threshold at zero plasma natural frequency in EF experiments is resolved by two-fluid simulations. We find that the very small island and smooth bifurcation in EF penetration near zero frequency is hard to detect in the experiment, leading to a finite penetration threshold within the capability of the experimental measurements. (paper)