Density rendering of the Kelvin-Helmholtz instability at t = 4 for N_smooth = 32 with the ISPH 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 (OI, 32) and the popular Wendland C₂ and C₄ kernels. We have selected three cases where discernible differences can be seen (n_x = 128, ∆ρ = 2; n_x = 64, ∆ρ = 2; n_x = 128, ∆ρ = 8). For the ∆ρ = 2 cases we observed that the C₂ and C₄ kernels exhibit more angular momentum errors (inherent to ISPH) compared to the O_I,32 kernel, where the inner stream becomes significantly twisted, deviating from the high resolution and high N_smooth results (see Appendix A). For the high density case n_x = 128, ∆ρ = 8, we observed that C₄ is unable to generate the same vortex structure in the upper plane of the stream and exhibit some asymmetry around the plane.