Upper panels: density (left) and radial velocity profiles (right) for the collapse of an initially isothermal sphere of gas at t = 0.8. The solid black line is the 1D-PPM solution. We show the SPHYNX calculations with p = 0 (red) and p = 1 (green) in Eq. (34). Calculations using GADGET-2 are in blue. Lower panels: profiles of | ⟨ Δr ⟩ | (left) and ∑ _bV_bW_ab (right) for p = 0 (red) and p = 1 (green).