Convergence study of the Gresho-Chan vortex with the ISPH method for N_smooth = 256. Here we plot the E₀ error versus the number of resolution elements in the x direction (n_x) at t = 3. Much lower zeroth order errors for the optimized kernel and C₂ kernel can be seen compared to the higher order C₄ kernel. Note here that even though being zeroth order (dependent on local particle order), the error still decreases with increasing resolution ($n_x^{-0.55}$) because the particle distribution becomes more uniform at higher resolution.