Comparison of three different implementations of the immersed boundary method in WRF (WRF-IBM)

The Weather Research and Forecasting model (WRF) is being used for atmospheric boundary layer flow at increasingly higher grid resolutions. As the grid resolution increases, so does the resolved terrain slope, posing a challenge to the terrain-following coordinates used by WRF and other mesoscale models. An immersed boundary method (IBM) was implemented into WRF (Lundquist et al. 2010, 2012). The IBM uses non-conforming coordinates with the terrain boundary “immersed” in the grid. Boundary conditions are set for grid cells intersected by the immersed surface.

This work extends the existing WRF-IBM model to implement appropriate flux boundary conditions based on Monin-Obukhov (M-O) similarity theory. Three different surface treatments are implemented at the immersed boundary, to develop an IB method which enforces M-O theory for atmospheric boundary layer applications. The surface treatments used in this work are all known as direct forcing, first used in the work of Mohd-Yusof (1997). With this method, the velocity or the shear stress value is modified at the points near the boundary to enforce the correct boundary condition. The first method is a ghost cell IBM method, where velocity is reconstructed at the ghost cell below the surface based on M-O similarity theory. The second method is also a ghost cell method, but instead of reconstructing velocity at the ghost cell, the shear stress is reconstructed. The third method is based on velocity reconstruction as in Fadlun et al [2000], where the velocity is reconstructed at the first fluid node according to the logarithmic profile. Validation test cases include pressure driven flow over flat terrain and an idealized valley with a neutral atmospheric boundary layer. The simulations will be used to evaluate the performance of the different surface treatments in WRF-IBM over complex terrain.