A linear model for neutral surface-layer flow over orography is presented. The Reynolds-Averaged Navier-Stokes and E - epsilon turbulence closure equations are expressed in a terrain-following coordinate system created from a simple analytical expression in the Fourier domain. The perturbation equations are solved spectrally horizontally and by numerical integration vertically. Non-dimensional solutions are stored in look-up tables for quick re-use. Model results are compared to measurements, as well as other authors' flow models in three test cases. The model is implemented and tested in two-dimensional space; the equations for a full three-dimensional version are presented.
Corbett, J-F., Ott, S., & Landberg, L. (2008). A mixed spectral-integration model for neutral mean wind flow over hills. Boundary-Layer Meteorology, 128(2), 229-254. https://doi.org/10.1007/s10546-008-9284-z