Line-driven disc wind models with an improved line force

We describe an efficient method of calculating the radiation pressure resul ting from spectral lines, including all the terms in the velocity gradient tensor. We apply this method to calculate the two-dimensional, time-depende nt structure of winds from luminous discs. Qualitative features of our new models are very similar to those we calculated including only the dominant terms in the tensor. In particular, we find that models which displayed uns teady behaviour in our earlier paper are also unsteady with the new method, and gross properties of the winds, such as mass-loss rate and characterist ic velocity, are not changed by the more accurate approach. The largest cha nge caused by the new method is in the disc-wind opening angle: winds drive n only by the disc radiation are more polar with the new method, whilst win ds driven by the disc and central object radiation are typically more equat orial. In the closing discussion, we provide further insight into the way t he geometry of the radiation field and consequent flow determine the time p roperties of the flow.