Density rendering of the Kelvin-Helmholtz instability at t=2 (left column) and t=4 (right column) for an initial density contrast of ∆ρ = 2 (top panels) and ∆ρ = 8 (bottom panels) with the GDSPH method. The X and Y axes have a length of one. Here one can see a comparison in the development of the instability between the optimized kernel at a given N_smooth and the popular Wendland C₂ and C₄ kernels. We observed a clear improvement in the optimized kernel, reproducing a similar behavior of the C₄ kernel at double the neighbor count (N_smooth). For the high density contrast ∆ρ = 8, there are only minor differences between the different kernels at N_smooth = 128. These can be compared to the higher resolution cases given in Appendix A.