A coupled immersed boundary method and wall modelling framework for high-Reynolds number flows over complex terrain

We present the development and validation of an immersed boundary method (IBM) along with a wall model (WM) to simulate atmospheric boundary-layer flows over complex terrain. The framework presented here has two novel aspects over standard IBM implementations. First, the underlying schemes are global in nature and require specification of values throughout the solid region. Second, to enable high-Reynolds number simulations, a wall model is coupled to the IBM. The proposed numerical framework is shown to have second-order accuracy. The framework is validated by simulating flow over a 2D as well as 3D cosine-squared hill and comparing to previously published experimental results. The mean velocity and turbulence intensity are reproduced accurately by our LES. The flow over the Bolund hill, marked by steep slopes which makes this a challenging test case, is also simulated and results are compared to field observations showing good agreement. The framework also accurately reproduces the turbulent statistics in the wake of a turbine situated on a flat terrain, with the flat terrain modelled using the IBWM framework, thus demonstrating its applicability to high-Reynolds number atmospheric and wind farm flows over complex terrain.