Current experiments are providing measurements of the flux power spectrum from the Lyman-alpha forests observed in quasar spectra with unprecedented accuracy. Their interpretation in terms of cosmological constraints requires specific simulations of at least equivalent precision. In this paper, we present a suite of cosmological N-body simulations with cold dark matter and baryons, specifically aiming at modeling the low-density regions of the inter-galactic medium as probed by the Lyman-a forests at high redshift. The simulations were run using the GADGET-3 code and were designed to match the requirements imposed by the quality of the current SDSS-III/BOSS or forthcoming SDSS-IV/eBOSS data. They are made using either 2 x 768(3) similar or equal to 1 billion or 2 x 192(3) similar or equal to 14 million particles, spanning volumes ranging from (25 Mpc h(-1))(3) for high-resolution simulations to (100 Mpc h(-1))(3) for large-volume ones. Using a splicing technique, the resolution is further enhanced to reach the equivalent of simulations with 2 x 3072(3) similar or equal to 58 billion particles in a (100 Mpc h(-1))(3) box size, i.e. a mean mass per gas particle of 1.2 x 10(5)M(circle dot)h(-1). We show that the resulting power spectrum is accurate at the 2% level over the full range from a few Mpc to several tens of Mpc. We explore the effect on the one-dimensional transmitted-flux power spectrum of four cosmological parameters (n(s), sigma(8), Omega(m), and H-0) and two astrophysical parameters (T-0 and gamma) that are related to the heating rate of the intergalactic medium. By varying the input parameters around a central model chosen to be in agreement with the latest Planck results, we built a grid of simulations that allows the study of the impact on the flux power spectrum of these six relevant parameters. We improve upon previous studies by not only measuring the effect of each parameter individually, but also probing the impact of the simultaneous variation of each pair of parameters. We thus provide a full secondorder expansion, including cross-terms, around our central model. We check the validity of the second-order expansion with independent simulations obtained either with different cosmological parameters or different seeds. Finally, a comparison to the one-dimensional Lyman-alpha forest power spectrum obtained with BOSS by [1] shows an excellent agreement.
