The aim of this study is to simulate the interaction of the solar wind with the Hermean magnetosphere when the interplanetary magnetic field is weak, performing a parametric study for all the range of hydrodynamic values of the solar wind predicted on Mercury for the ENLIL + GONG WSA + Cone SWRC model: density from 12 to 180 cm −3 , velocity from 200 to 500 km/s and temperatures from 2 · 10 4 to 18 · 10 4 K, and compare the results with a real MESSENGER orbit as reference case. We use the code PLUTO in spherical coordinates and an asymmetric multipolar expansion for the Hermean magnetic field. The study shows for all simulations a stand off distance larger than the Mercury radius and the presence of close magnetic field lines on the day side of the planet, so the dynamic pressure of the solar wind is not high enough to push the magnetopause on the planet surface if the interplanetary magnetic field is weak. The simulations with large dynamic pressure lead to a large compression of the Hermean magnetic field modifying Email address: deviriam@gmail.com (telf: +33782822476) (J. Varela) Preprint submitted to Elsevier March 17, 2016 its topology in the inner magnetosphere as well as the plasma flows from the magnetosheath towards the planet surface.