A detailed computational study of the wavelength-dependent efficiency of optical second-harmonic generation in plasmonic nanostructures is presented. The computations are based on a discontinuous Galerkin Maxwell solver that utilizes a hydrodynamic material model to calculate the free-electron dynamics in metals without any further approximations. Besides wave-mixing effects, the material model thus contains the full nonlocal characteristics of the electromagnetic response, as well as intensity-dependent phenomena such as the Kerr effect.