  Cosmological hydrodynamic simulations can accurately predict the properties
of the intergalactic medium (IGM), but only under the condition of retaining
high spatial resolution necessary to resolve density fluctuations in the IGM.
This resolution constraint prohibits simulating large volumes, such as those
probed by BOSS and future surveys, like DESI and 4MOST. To overcome this
limitation, we present Iteratively Matched Statistics (IMS), a novel method to
accurately model the Lyman-alpha forest with collisionless N-body simulations,
where the relevant density fluctuations are unresolved. We use a small-box,
high-resolution hydrodynamic simulation to obtain the probability distribution
function (PDF) and the power spectrum of the real-space Lyman-alpha forest
flux. These two statistics are iteratively mapped onto a pseudo-flux field of
an N-body simulation, which we construct from the matter density. We
demonstrate that our method can perfectly reproduce line-of-sight observables,
such as the PDF and power spectrum, and accurately reproduce the 3D flux power
spectrum (5-20%). We quantify the performance of the commonly used Gaussian
smoothing technique and show that it has significantly lower accuracy (20-80%),
especially for N-body simulations with achievable mean inter-particle
separations in large-volume simulations. In addition, we show that IMS produces
reasonable and smooth spectra, making it a powerful tool for modeling the IGM
in large cosmological volumes and for producing realistic "mock" skies for
Lyman-alpha forest surveys.
