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HSIM simulates observations with HARMONI on the Extremely Large Telescope. HSIM takes high spectral and spatial resolution input data cubes, encoding physical descriptions of astrophysical sources, and generates mock observed data cubes. The simulations incorporate detailed models of the sky, telescope, instrument, and detectors to produce realistic mock data. HSIM performs in-depth simulations for several key science cases as part of the design and development of the HARMONI integral field spectrograph, including the ELT AO performance, atmospheric effects and realistic detector statistics.