The algebraic variational multiscale–multigrid method, an advanced computational approach recently proposed for large-eddy simulation of turbulent flow, is further developed in this study for turbulent flow simulations in complex geometries. In particular, it is applied to the complex case of pulsatile turbulent flow dynamics of the upper and lower pulmonary airways up to generation 7 and carefully investigated for this important application. Among other things, the results obtained with the proposed method are compared with the results obtained with a rather traditional stabilized finite element method. As opposed to previous large-eddy simulations of pulmonary airways, we consider a pulsatile inflow condition, allowing the development of turbulence over a pulse cycle to be investigated, which obviously makes these results more physiologically realistic. Our results suggest that turbulent effects in the bronchial airways are rather weak and can completely decay as early as the third generation, depending on geometry and flow distribution. Both methods utilized in this study are able to adequately capture all flow stages from laminar via transitional to turbulent regimes without any modifications. However, the algebraic variational multiscale–multigrid method provides superior results as soon as the flow enters the most challenging, turbulent flow regime. Furthermore, the robustness of the scale-separation approach based on plain aggregation algebraic multigrid inherent to the algebraic variational multiscale–multigrid method is demonstrated for the present complex geometry. Copyright © 2012 John Wiley & Sons, Ltd.