Density rendering of the Kelvin-Helmholtz instability (∆ρ = 8) at t = 2 (three left columns) and t = 4 (three right columns) for varying resolution (n_x = 64,128,256), N_smooth = 32,64,128, and method (GDSPH upper three rows and ISPH bottom three rows). The X and Y axis have a length of 1. These simulations were all run with the optimized kernel for each O_Nsmooth GDSPH and O_I,Nsmooth for ISPH. Similar as the low density version of Fig. A.1, we can see that ISPH captures instability well regardless of neighbor number. We can see additional diffusion from the ISPH runs compared to the GDSPH runs, even with the highest resolution. There also seem to be additional noise in the small-scale density structures as we increase the number of neighbors for ISPH. Potentially related to the issue found in Fig. A.3