Convergence study of the Gresho-Chan vortex with the GDSPH method for N_smooth = 32,64,128,256. Here we plot the L_1,error over resolution elements in the x direction (n_x) at t = 3. Significant improvements can be seen for all optimized kernels compared to the Wendland C2 and C4 kernels. The kernels were optimized in respect to an earlier time t = 1 and we can see that O₂₅₆ have an improved result over O₁₂₈ for N_smooth = 128 at this later time, even beating out O₆₄ for N_smooth = 64 at higher resolution (n_x > 128). The C4 kernel exhibits slightly better convergence slope at high N_smooth and n_x > 128, likely due to it’s higher order properties (fewer O(h²) errors).