We present the first results from a project to model the prestellar cores in Ophiuchus, using initial conditions constrained as closely as possible by observation. The prestellar cores in Ophiuchus appear to be evolving in isolation - in the sense that the timescale on which an individual prestellar core collapses and fragments is estimated to be much shorter than the timescale on which it is likely to interact dynamically with another core. Therefore it is realistic to simulate individual cores separately, and this in turn makes it feasible (a) to perform multiple realisations of the evolution of each core (to allow for uncertainties in the initial conditions which persist, even for the most comprehensively observed cores), and (b) to do so at high resolution (so that even the smallest protostars are well resolved). The aims of this project are (i) to address how best to convert the observations into initial conditions; (ii) to explore, by means of numerical simulations, how the observed cores are likely to evolve in the future; (iii) to predict the properties of the protostars that they will form (mass function, multiplicity statistics, etc.); and (iv) to compare these properties with the properties of the observed pre-Main Sequence stars in Ophiuchus. We find that if the observed non-thermal velocities in the Ophiuchus prestellar cores are attributed to purely solenoidal turbulence, they do not fragment; they all collapse to form single protostars. If the non-thermal velocities are attributed to a mixture of solenoidal and compressive turbulence, multiple systems form readily. The turbulence first generates a network of filaments, and material then tends to flow along the filaments, at first into a primary protostar, and then onto a compact accretion disc around this protostar; secondary protostars condense out of the material flowing into the disc along the filaments. If the turbulence is purely solenoidal, but part of the non-thermal velocity dispersion is attributed to solid-body rotation, then again multiple systems form readily, but the pattern of fragmentation is quite different. A primary protostar forms near the centre of the core, and then an extended accretion disc forms around the primary protostar, and eventually becomes so massive that it fragments to produce low-mass secondaries; these frequently end up in hierarchical multiple systems.