  Since the launch on 2018/08/12, Parker Solar Probe (PSP) has completed its
first and second orbits around the Sun, having reached down to 35.7 solar radii
at each perihelion. In anticipation of the exciting new data at such
unprecedented distances, we have simulated the global 3D heliosphere using an
MHD model coupled with a semi-empirical coronal model using the best available
photospheric magnetograms as input. We compare our heliospheric MHD simulation
results with in situ measurements along the PSP trajectory from its launch to
the completion of the second orbit, with particular emphasis on the solar wind
structure around the first two solar encounters. Furthermore, we show our model
prediction for the third perihelion, which occurred on 2019/09/01. Comparison
of the MHD results with PSP observations provides a new insight on the solar
wind acceleration. Moreover, PSP observations reveal how accurately the
ADAPT-WSA predictions work throughout the inner heliosphere.
