2.5D Particle simulations of the solar wind interaction with the magnetized regions on the surface of the Moon confirm the earlier 2D MHD result that mini-magnetospheres can form around the magnetic anomalies. A dipole buried 100 km below the surface with a field strength equal to 50 nT at the surface and 10 nT at 100 km above the surface held the solar wind off of the surface and caused a bow shock and a magnetopause to form. However, the boundary separating the bow shock and magnetopause becomes ambiguous as the two structures merge due to the small-scale size of the mini-magnetospheres. Acceleration of solar wind particles occurs at the shock. Inside the magnetopause, the Lunar electrons remained highly magnetized and exhibited fluid-like behavior. The Lunar ions, on the other hand, become demagnetized. Outside of the magnetopause, the solar wind ions and electrons exhibited fluid-like behavior. Small-scale and nonideal MHD effects can be included into fluid simulations by adding Hall and pressure gradient terms in Ohm's Law, creating a magnetoplasma dynamics (MPD) model. The small-scale effects allow for field-aligned currents and electric fields that look qualitatively similar to those in the particle simulations, but they do not appear to change the overall shape of the mini-magnetosphere. The extra components of the electric field indicate the presence of charge separation at the shock surface, due to the momentum difference between ions and electrons, and the near the Lunar surface, due to nonideal MHD behavior inside the mini-magnetosphere. The 2.5D MPD model can replicate the ion demagnetization seen in the 2.5D particle simulations.