During Parker Solar Probe's first orbit, the solar wind plasma was observed in situ closer than ever before, the perihelion on 2018 November 6 revealing a flow that is constantly permeated by large-amplitude Alfvénic fluctuations. These include radial magnetic field reversals, or switchbacks, that seem to be a persistent feature of the young solar wind. The measurements also reveal a very strong, unexpected, azimuthal velocity component. In this work, we numerically model the solar corona during this first encounter, solving the MHD equations and accounting for Alfvén wave transport and dissipation. We find that the large-scale plasma parameters are well reproduced, allowing the computation of the solar wind sources at Probe with confidence. We try to understand the dynamical nature of the solar wind to explain both the amplitude of the observed radial magnetic field and of the azimuthal velocities.