  The Multi-channel Photometric Survey Telescope (Mephisto) is a real-time,
three-color photometric system designed to capture the color evolution of stars
and transients accurately. This telescope system can be crucial in cosmological
distance measurements of low-redshift (low-$z$, $z$ $\lesssim 0.1$) Type Ia
supernovae (SNe Ia). To optimize the capabilities of this instrument, we
perform a comprehensive simulation study before its official operation is
scheduled to start. By considering the impact of atmospheric extinction,
weather conditions, and the lunar phase at the observing site involving the
instrumental features, we simulate the light curves of SNe Ia obtained by the
Mephisto. The best strategy in the case of SN Ia cosmology is to take the image
at an exposure time of 130 s with a cadence of 3 days. In this condition,
Mephisto can obtain hundreds of high-quality SNe Ia to achieve a distance
measurement better than $4.5\%$. Given the on-time spectral classification and
monitoring of the Lijiang 2.4 m Telescope at the same observatory, Mephisto, in
the whole operation, can significantly enrich the well-calibrated sample of
supernovae at low-$z$ and improve the calibration accuracy of high-$z$ SNe Ia.
