Radial slice of the accreted mass surface density at 50 orbits for κ = 5. Rows correspond to the models Γ₀, Γ₂, Γ₄, and Γ₈ from top to bottom. Left column: Simulations employing the negative radial velocity condition. Right column: Simulations using the bound material condition. The maps are extracted on a spherical shell at R = 0.15 r_H. The color scale indicates the accreted mass per unit area in units of M_jup au⁻². Overlaid contours show the mass flux, with signs defined according to Eq. (21).