Amplitude of the k = 2π mode over time for different smoothing kernels and density contrasts: ∆ρ = 2 (top) and ∆ρ = 8 (bottom). The ISPH method shows little difference between the different smoothing kernels, capturing a growth rate of roughly γ ∝ π in ∆ρ = 2 case and a slightly lower growth rate for ∆ρ = 8 (as expected). The GDSPH method of N_smooth = 64 struggles to capture the same growth rate as the ISPH method, but we observed that the optimized kernel improves the growth rate of the KH mode for both ∆ρ = 2 and ∆ρ = 8.