A numerical study on the 2009 Mw 6.3 L’Aquila earthquake is here presented using a high‐performance spectral element (SE) code to clarify the issues regarding the generation of physics‐based deterministic ground‐motion scenarios in near‐fault conditions and over a broad range of frequencies. Numerical simulations provide reliable ground‐motion scenarios up to about 2.5 Hz in the epicentral region of the L’Aquila earthquake, as confirmed by the good agreement between the simulated peak ground velocity (PGV) wave field and the observed distribution of damage. Moreover, the synthetic waveforms fit reasonably well the strong‐motion recordings within the town of L’Aquila and the surrounding areas. Nevertheless, some discrepancies are found in the upper Aterno Valley, associated to a considerable extent with the details of the rupture process. Improvements on the source modeling are obtained through the definition of stochastically (but realistically) varying kinematic source parameters that may play a relevant role in propagating high‐frequency (HF) components of ground motion, poorly controlled by numerical approaches. Finally, the proposed hybrid scheme to generate broadband (BB) synthetic waveforms, by combining the low‐frequency (LF) synthetics from SE simulations (f<2.5 Hz) with HF stochastic components, appears as a powerful tool to generate ground‐shaking scenarios over the whole frequency range of interest for engineering applications.