We numerically simulate the performance of the ultrasimple frequency-resolved-optical-gating (FROG) technique, GRENOUILLE, for measuring ultrashort laser pulses. While simple in practice, GRENOUILLE has many theoretical subtleties because it involves the second-harmonic generation of relatively tightly focused and broadband pulses. In addition, these processes occur in a thick crystal, in which the phase-matching bandwidth is deliberately made narrow compared to the pulse bandwidth. In these simulations, we include all sum-frequency-generation processes, both collinear and noncollinear. We also include dispersion using the Sellmeier equation for the crystal BBO. Working in the frequency domain, we compute the GRENOUILLE trace for practical-and impractical- examples and show that accurate measurements are easily obtained for properly designed devices.