Intercomparison of Terrain-Following Coordinate Transformation and Immersed Boundary Methods for Large-Eddy Simulation of Wind Fields over Complex Terrain

The ability to predict accurately turbulent wind fields over complex terrain plays an important role in a number of environmental and engineering applications such as urban air pollution prediction, local weather forecasting in mountainous regions, wind energy potential assessment and optimal micro-siting of wind turbines. Large-eddy simulation (LES) has become an important tool for simulating turbulent flows, largely due to the fact that LES is superior to the conventional Reynolds-averaged Navier-Stokes approach in predicting unsteady turbulent behaviors, and computationally more efficient than direct numerical simulation. Recently the development and application of LES-based numerical models for wind field simulation is on the rise. So far satisfactory results have been reported mainly for cases where the terrain is flat. Complex terrain, especially steep terrain, remains a challenge for wind flow modeling in general.

For a long time, the terrain-following coordinate transformation method (TFCT) has been used in both mesoscale models and LES models to represent topography effects. TFCT allows an irregular bottom boundary to be mapped to a Cartesian grid so that application of bottom boundary conditions is simplified. While this aspect is advantageous, TFCT has the disadvantage of introducing additional terms in the governing equations, and some corresponding numerical errors in the presence of any slope. For slopes lower than 30 degrees those errors are negligible, but at higher slopes model errors become large and can cause stability problems. Recently, the immersed boundary method (IBM) has been implemented in LES models to represent steep terrain encountered in mountainous regions. The advantage of IBM is that it offers a simple strategy to use a regular computational grid while solving flow problems with complex geometry. Interpolation methods are used in IBM to represent the effect of the boundary on the flow. In addition to no-slip boundary condition, in practice, a wall model based on the Monin-Obukhov similarity theory is usually adopted when applying IBM to LES, due to impractical refinement of the whole regular grid in order to resolve the near-wall region, and the lack of an accurate wall model applicable for rough surfaces. However, implementation of such a wall model in the context of IBM is not as straightforward as that in TFCT, and commonly used approaches such as smearing and linear interpolation could introduce non-negligible errors.

We here perform an intercomparison of TFCT and IBM for large-eddy simulation of a turbulent wind field over a three-dimensional hill, for which wind-tunnel measurements are available for validation. The experimental dataset contains both vertical and horizontal profiles of mean velocities and variances, which allows an in-depth comparison of the numerical models. For the TFCT, a new algorithm for solving the pressure Poisson equation in the transformed coordinate system is proposed and first validated for a laminar flow over periodic two-dimensional hills by comparing with available benchmark solutions. Since the slopes of the three-dimensional hill are not steep, TFCT, which is free from implementation errors for the wall model, is preferable to IBM. The effects of sub-grid scale models and different schemes used to implement wall boundary conditions for IBM are studied. Discrepancies between the results obtained by TFCT and IBM are observed near the surface. The source of errors and possible ways to improve the IBM implementation are discussed.