Nanowire-based transistors represent a promising design for truly nanoscaled devices and can be used as active elements in sensor applications for the detection of biological or inorganic species in solution. For a full understanding of the interplay of electronic, mechanical and chemical properties of the device in different regimes and under the influence of different parameters governing the transport properties observed in experiment, a thorough and scale-bridging simulation platform is required. We present a theoretical framework for the calculation of charge transport through nanowire-based Schottky-barrier field-effect transistors capturing the relevant mechanisms of the transport processes. Our calculations bridge and unify two approaches on different length scales: (1) the finite element method is used to model realistic device geometries and to calculate the electrostatic potential across the Schottky barrier by solving the Poisson-Boltzmann equation, and (2) the Landauer-Büttiker approach combined with the method of non-equilibrium Green's functions is employed to calculate the charge transport through the device. Our model correctly reproduces typical I V characteristics of field-effect transistors, and the dependence of the saturated drain current on the gate field and the device geometry are in good agreement with experiments. Our approach is suitable for one-dimensional Schottky-barrier field-effect transistors of arbitrary device geometry and it is intended to be a powerful and reliable simulation platform for the development of nanowire-based sensors.