Rapid mass transfer preceding a common envelope event is a critical yet poorly understood stage of binary stellar evolution, setting the initial conditions for the common envelope inspiral and for the formation of compact binary stars. We present three-dimensional smoothed particle hydrodynamics simulations of accretion disk formation during this phase using the Phantom code. We model the final 21 yr of Roche lobe overflow from a 7 M_⊙ red giant onto a 1.4 M_⊙ neutron star companion, with the mass transfer rate prescribed by a 1D MESA model. Over this interval, the mass transfer rate increases from 1.3×10⁻⁴ to 1.0×10⁻¹ M_⊙ yr⁻¹. An accretion disk forms around the neutron star, reading a mass of 5.0×10⁻³ M_⊙, a radius of 40 R_⊙ and an aspect ratio H/R∼ 0.1 by the end of the simulation. A direct comparison with the grid-based simulation of Juarez-Garcia et al. (2025) shows that the two codes produce disk masses that agree to within 6%. The accretion rate onto the neutron star reaches 5.2×10⁻³ M_⊙ yr⁻¹, corresponding to 14% of the mass injection rate and greatly exceeding the Eddington limit. We demonstrate that this accretion rate is consistent with being driven by turbulent angular momentum transport, with an effective viscosity parameter α_(rm eff) = 0.03-0.06. Ejecta leaving the binary system carries specific angular momentum approximately 90% that of the L₂ Lagrange point, equivalent to ∼10 times the binary's specific orbital angular momentum. This indicates that L₂ mass loss efficiently reduces the binary orbital separation.