  Parker Solar Probe (PSP) is providing an unprecedented view of the Sun's
corona as it progressively dips closer into the solar atmosphere with each
solar encounter. Each set of observations provides a unique opportunity to test
and constrain global models of the solar corona and inner heliosphere and, in
turn, use the model results to provide a global context for interpreting such
observations. In this study, we develop a set of global magnetohydrodynamic
(MHD) model solutions of varying degrees of sophistication for PSP's first four
encounters and compare the results with in situ measurements from PSP,
Stereo-A, and Earth-based spacecraft, with the objective of assessing which
models perform better or worse. All models were primarily driven by the
observed photospheric magnetic field using data from Solar Dynamics
Observatory's Helioseismic and Magnetic Imager (HMI) instrument. Overall, we
find that there are substantial differences between the model results, both in
terms of the large-scale structure of the inner heliosphere during these time
periods, as well as in the inferred time-series at various spacecraft. The
"thermodynamic" model, which represents the "middle ground", in terms of model
complexity, appears to reproduce the observations most closely for all four
encounters. Our results also contradict an earlier study that had hinted that
the open flux problem may disappear nearer the Sun. Instead, our results
suggest that this "missing" solar flux is still missing even at 26.9 Rs, and
thus it cannot be explained by interplanetary processes. Finally, the model
results were also used to provide a global context for interpreting the
localized in situ measurements.
