  We present HSIM: a dedicated pipeline for simulating observations with the
HARMONI integral field spectrograph on the European 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
and instrument to produce realistic mock data. Further, we employ a new method
of incorporating the strongly wavelength dependent adaptive optics point spread
functions. HSIM provides a step beyond traditional exposure time calculators
and allows us to both predict the feasibility of a given observing programme
with HARMONI, as well as perform instrument design trade-offs. In this paper we
concentrate on quantitative measures of the feasibility of planned
observations. We give a detailed description of HSIM and present two studies:
estimates of point source sensitivities along with simulations of star-forming
emission-line galaxies at $z\sim 2-3$. We show that HARMONI will provide
exquisite resolved spectroscopy of these objects on sub-kpc scales, probing and
deriving properties of individual star-forming regions.
