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An improved immersed boundary method for atmospheric boundary layer simulations over complex terrain


Accurately simulating flow over complex terrain has long been a challenging scientific problem.As computational power increases, atmospheric simulations are pushed toward higher resolutions with enough computational resources to better resolve complex topography. Turbulence and flow dynamics which decades ago could not be resolved (e.g. drainage flow over a steep mountain) can now be studied using computational tools. The Weather Research and Forecasting (WRF) model is a numerical weather prediction and atmospheric research model that can be used in a wide range of grid resolutions from mesoscale weather prediction (km scale) to large-eddy simulation for atmospheric boundary layer studies (∼100 m and finer scales). The WRF model uses terrain-following coordinates, which is adequate for mesoscale models where the details of the terrain are not well resolved and the terrain slope is not very steep. With increased resolution, resolved terrain slopes become steeper, and the native terrain-following coordinates used in WRF result in numerical errors and instability. To eliminate these numerical errors and instability, but still be able to use WRF’s grid nesting strategy to include weather effects for complex terrain simulation, an immersed boundary method was implemented into WRF by Lundquist et al. (2010, 2012). The immersed boundary method uses a non-conforming grid where the terrain surface is immersed into the grid. The immersed boundary conditions are enforced by adding an additional forcing term to the Navier-Stoke equations for the points near the immersed boundary. The original immersed boundary method in WRF-IBM uses a no-slip boundary condition, which is suitable for urban simulations with fine resolution (1 m). The no-slip boundary condition is not appropriate for atmospheric simulations at 100 m scale, where the surface layer and the underlying topography are not extremely well resolved.This dissertation focuses on the development of improved log-law boundary conditions forWRF-IBM to enable atmospheric simulations over complex terrain at horizontal resolutions on the order of 100 m. First an existing velocity-reconstruction immersed boundary method (VR-IBM)is implemented into WRF. The VR-IBM is tested extensively for flat terrain, an idealized hill, and flow over Askervein Hill. At very fine resolutions, VR-IBM performs well, but further tests show some limitations at intermediate resolutions, where VR-IBM for example develops spatial1

oscillations. Other limitations are found for VR-IBM and another shear-stress reconstruction (SR-IBM) approach depending on resolution and grid aspect ratios (see also Arthur et al., 2019). Next, a new hybrid log-law boundary condition for IBM (HYBRID-IBM) is developed and implemented into WRF. This hybrid method is evaluated against VR-IBM and SR-IBM for a wide range of idealized cases (both flat terrain and idealized 3D hill at different slopes and resolutions) and real cases, including Askervein hill (intermediate resolutions) and Bolund hill (steep slope, fine resolution). Sensitivity tests of the three IBM approaches are performed to examine the effects of the location where terrain intersects with the grid, the grid aspect ratio, the grid resolution, and the terrain slope.Based on our knowledge, this work is the first time a log-law boundary condition has been used with the immersed boundary method and WRF to enable simulations of atmospheric flow at intermediate resolutions. This work also represents the first time that several IBM methods, including the VR-IBM, SR-IBM, and HYBRID-IBM have been validated using a large number and variety of test cases. Specifically, these methods have been tested not only in comparison to theory(flat terrain), but also to observations (Askervein and Bolund Hills) and through direct comparison to WRF results using the native terrain-following coordinate (for the flat terrain, idealized hill and Askervein Hill cases). Furthermore, this dissertation makes a first attempt toward a robust evaluation of the different IBM approaches, using test cases with different resolutions, different terrain slopes, different aspect ratios and different grid setups, to demonstrate the robustness and sensitivity of implementation for the different methods. In almost all test cases, the HYBRID-IBM approach outperforms the other methods. This series of test cases provides rigorous validation of all three IBM methods and thus conclusions about the advantages and disadvantages of different methods can be made.

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