Abstract The interpretation of multi-spacecraft heliospheric observations and three-dimensional reconstruction of the structured and evolving solar wind with propagating and interacting coronal mass ejections (CMEs) is a challenging task. Numerical simulations can provide global context and suggest what may and may not be observed. The Community Coordinated Modeling Center (CCMC) provides both mission science and space weather support to all heliospheric missions. Currently, this is realized by real-time simulations of the corotating and transient disturbances by the WSA-ENLIL-Cone model. We have simulated the heliospheric space weather relevant to the Parker Solar Probe (PSP) mission since 2018 September and provided numerical results to our colleagues analyzing in situ measurements published in the ApJS Special Issue. In this paper, we do not analyze PSP data, but we present recent updates in simulating the background solar wind and compare them with an existing operational model around the first PSP Perihelion, from 2018 October to 2018 December. We introduce new tools that assist in the interpretation of remote observations and in situ measurements useful for PSP and other missions, and for predicting heliospheric space weather. We also use this opportunity to evaluate recent improvements in the WSA and ADAPT-WSA coronal models that are being transitioned and considered to be transitioned, respectively, to operations. Finally, we simulate CME-like hydrodynamic ejecta with various parameters and calculated synthetic white-light images that can be used for “mid-course” correction of operational predictions.