An immersed boundary method for flow over complex terrain

Most mesoscale numerical models use terrain-following coordinates to accommodate complex terrain. Terrain-following 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 additional numerical truncation errors. Terrain-following coordinates are typically unable to handle terrain surfaces steeper than 45 degrees; mesoscale models sometimes fail with even shallower terrain slopes.

Here we introduce an alternative gridding 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. Boundary conditions are imposed on the immersed surface for velocities and scalar quantities through interpolation. This presentation illustrates the behavior of IBM-WRF using idealized cases of pressure-driven and thermally-induced flows over two-dimensional terrain. Comparisons are made between simulations using standard terrain-following coordinates and those using IBM. The scalar transport test case of Schaer et al. (2002) is used to illustrate the reduction of numerical errors far above the terrain surface. Extension to three dimensions and the inclusion of mesoscale physics parameterizations are described in a companion abstract (Daniels et al. 2008).