High-fidelity transient simulations of turbulent flows usually require highly resolved grids, leading to unacceptable large computational wall times even on large supercomputers. In an attempt to address this limitation, a hybrid Large-Eddy/Reynolds-Averaged scale-adaptive turbulence model has been applied together with a Volume-Of-Fluid (VOF) solver in OpenFOAM to simulate cavitation in the injector nozzle and primary fuel atomization during the opening event of a GDI gasoline-injector for automotive applications. A dynamic mesh strategy based on topological changing grids has been used to handle the moving geometry. In addition, algorithmic developments are presented to improve parallel performance on modern supercomputers. The outcome of the scalability tests are reported together with results from simulations on the Continental XL3.0 6-hole injector performed at the Argonne National Laboratory.