L₁ calculation of the errors in the numerical experiments shown in Fig. 2. Left: averaged value of L₁ for the partition of the unity (solid lines) and ⟨Δx⟩/h (dotted lines). Blue lines are for the estimator X₁ and magenta lines for X₂. Right: averaged value of L₁, obtained with Eq. (26), for the derivative of the wall function calculated with X₁ (solid blue line) and X₂ (solid magenta line). The black line is the calculation with the non-conservative ISPH, which is independent of the particular value of the exponent p. We note that when p ≃ 1 both schemes (ISPH and ncISPH) converge, albeit faster for estimator X₁ than for X₂.