Convergence study of the Gresho-Chan vortex with the ISPH method for N_smooth = 32,64,128,256. Here we plot the L_1,error over the resolution elements in the x direction (n_x) at t = 3. Significant improvements can be seen for the optimized kernels at N_smooth = 32,64 compared to the Wendland C2 and C4 kernels. While at higher N_smooth, there is much less difference between all the kernels. The kernels were optimized in respect to an earlier time, t = 1, and we observed that C₄ performs better at this later time for N_smooth = 256 than all the optimized kernels at all resolutions. This is surprising, as E₀ errors of the optimized kernels are much lower than the C₄ kernel (see Fig. 9), which might indicate that long-term behavior at this N_smooth is heavily determined by the higher order errors (O(h²)).