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Petascale computing will allow astrophysicists to investigate astrophysical objects, systems, and events that cannot be studied by current observational means and that were previously excluded from computational study by sheer lack of CPU power and appropriate codes. Here we present a pragmatic case study, focussing on the simulation of gamma-ray bursts as a science driver for petascale computing. We estimate the computational requirements for such simulations and delineate in what way petascale and peta-grid computing can be utilized in this context.