9A.5 An Immersed Boundary Method for Flow Over Complex Terrain
Most mesoscale numerical models use terrain-following coordinates to accommodate complex terrain. Terrain-following or sigma coordinates conform to the bottom topography and the coordinate lines gradually become smoother and flatter with distance from the ground. With very steep terrain, the coordinate lines retain a signature of the underlying surface shape even very far away from the ground. Coordinate transformations are introduced into the discretized equations and produce numerical truncation errors in addition to those associated with the chosen discretization scheme. Several methods have been proposed to reduce the truncation error arising from terrain-following coordinates. Schar et al. [2002] proposed a modified sigma coordinate in which grid distortion due to small scale terrain features decays with height more rapidly than distortion caused by large scale features. The modified coordinate flattens quickly with height and improves the accuracy of the solution. Klemp et al. [2003] investigated the errors that arise when numerical treatment of the metric terms is inconsistent with the discretization of other terms in the governing equations. Distortion seen in topographically induced gravity waves was reduced with consistent numerical treatment. Adcroft et al. [1997] used a shaved cell approach to represent topography on a Cartesian grid. This method eliminates grid distortion, but introduces complications in the numerical solution at the ground because the computational cells must be modified (shaved) where they intersect the topography. Here we introduce an alternative griding technique for flow over complex terrain using an immersed boundary method (IBM) in the Weather Research and Forecasting (WRF) model. With this method, the terrain surface intersects the grid, and variables are adjusted near the immersed boundary so that the flow is diverted by the boundary. Grid distortion and the associated truncation errors are thus avoided. Additionally, the method does not require modification of the computational stencil in the vicinity of the topography. Boundary conditions are imposed on the immersed surface for velocities and scalar quantities through interpolation. The implementation and validation of IBM in WRF in two dimensions has been described previously by Lundquist et al. [2007, 2008]. Here we focus on the behavior of the flow far above steep topography. A description of the WRF model, its native sigma coordinate, and the alternative immersed boundary method are provided in section 2. The scalar transport test case of Schar et al. [2002] is presented in section 3. Comparisons are made between simulations using standard terrain-following coordinates and those using IBM. Large truncation errors are present in the native coordinate, and it is demonstrated that the immersed boundary method can be used within WRF to alleviate these errors. Truncation errors can be attributed to either the finite differencing scheme or the metric terms. Further analysis in section 4 apportions the error attributable to each cause.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 945661
- Report Number(s):
- LLNL-CONF-406166; TRN: US200903%%709
- Resource Relation:
- Conference: Presented at: 13th Conference on Mountain Meteorology, Whistler, Canada, Aug 11 - Aug 15, 2008
- Country of Publication:
- United States
- Language:
- English
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