We have carried out direct numerical simulations (DNS) of the flow over a wing with 45° sweep and -4° angle-of-attack. On the upper wing side, a substantial cross flow creates ideal conditions for the study of cross-flow instability. Our simulation models a wind-tunnel experiment carried out at the Arizona State University (ASU), where 6μm high roughness cylinders were used to excite steady cross-flow vortices. We have successfully reproduced the linear growth rate of these vortices, whereas the receptivity amplitude obtained from our DNS is 40% of that measured in the experiment. Possible reasons for this discrepancy have been investigated by refining the roughness model of the DNS on the one hand, and, on the other hand, by carefully comparing the results from the DNS and the experiment with solutions to the parabolized stability equations (PSE). Good agreement between all approaches could be obtained when assuming a roughness height of 15μm. This suggests that the roughness cylinders in the experiment might have been slightly higher than 6μm, or that natural roughness might have contributed to the receptivity. Moreover, small differences in the pressure distribution or the presence of weak free-stream fluctuations in the wind tunnel may explain the larger modal amplitude measured in the ASU experiment.