The computational fluid dynamics of hurricane rapid intensification (RI) is examined through idealized simulations using two codes: a community-based, finite-difference/split-explicit model (WRF) and a spectral-element/semi-implicit model (NUMA). The focus of the analysis is on the effects of implicit numerical dissipation (IND) in the energetics of the vortex response to heating, which embodies the fundamental dynamics in the hurricane RI process. The heating considered here is derived from observations: four-dimensional, fully nonlinear, latent heating/cooling rates calculated from airborne Doppler radar measurements collected in a hurricane undergoing RI. The results continue to show significant IND in WRF relative to NUMA with a reduction in various intensity metrics: (1) time-integrated, mean kinetic energy values in WRF are ~20% lower than NUMA and (2) peak, localized wind speeds in WRF are ~12m/s lower than NUMA. Values of the eddy diffusivity in WRF need to be reduced by ~50% from those in NUMA to produce a similar intensity time series. Kinetic energy budgets demonstrate that the pressure contribution is the main factor in the model differences with WRF producing smaller energy input to the vortex by ~23%, on average. The low-order spatial discretization of the pressure gradient in WRF is implicated in the IND. In addition, the eddy transport term is found to have a largely positive impact on the vortex intensification with a mean contribution of ~20%. Overall, these results have important implications for the research and operational forecasting communities that use WRF and WRF-like numerical models.