Improving the immersed boundary method in WRF for complex mountainous terrain

The Weather Research and Forecasting model (WRF) is being used over complex terrain at increasingly higher grid resolutions. As the grid resolution increases, so does the resolved terrain slope, posing a challenge to the traditional terrain-following coordinates used by WRF and other mesoscale models. An immersed boundary method (IBM) was implemented into WRF (Lundquist et al. 2010, 2012), to alleviate numerical errors associated with steep terrain slopes. The IBM uses non-conforming coordinates with the terrain boundary “immersed” within the grid. Boundary conditions are set through interpolation procedures for grid cells intersected by the immersed surface. The WRF-IBM model has been validated for canonical flows and real urban cases using a no-slip bottom boundary condition.

In this work, we extend the existing WRF-IBM model to include a wall model at the terrain surface. This enables simulations over complex terrain, at resolutions where a no-slip boundary condition is not appropriate. The wall model implementation specifies boundary conditions at the wall in accordance with Monin-Obukhov similarity theory.

This work validates the log-law implementation in WRF-IBM by comparing WRF and WRF-IBM solutions for idealized flows. Validation test cases include pressure driven flow over flat terrain and idealized small amplitude Gaussian hills. Further simulations will be generated with real, complex terrain, and validated with field data.