We have carried out radiation-hydrodynamic simulations of thermally-driven accretion disc winds in low-mass X-ray binaries. Our main goal is to study the luminosity dependence of these outflows and compare with observations. The simulations span the range $rm{0.04 leq L_{acc}/L_{Edd} leq 1.0}$ and therefore cover most of the parameter space in which disc winds have been observed. Using a detailed Monte Carlo treatment of ionization and radiative transfer, we confirm two key results found in earlier simulations that were carried out in the optically thin limit: (i) the wind velocity -- and hence the maximum blueshift seen in wind-formed absorption lines -- increases with luminosity; (ii) the large-scale wind geometry is quasi-spherical, but observable absorption features are preferentially produced along high-column equatorial sightlines. In addition, we find that (iii) the wind efficiency always remains approximately constant at $rm{dot{M}_{wind}/dot{M}_{acc} simeq 2}$, a behaviour that is consistent with observations. We also present synthetic Fe XXV and Fe XXVI absorption line profiles for our simulated disc winds in order to illustrate the observational implications of our results.
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