Atmospheric transport over terrain

Almost all operational weather forecast models represent terrain using terrain-following meshes that become highly-distorted over steep slopes.  An alternative is the cut cell method but, while cut cell meshes are less distorted compared to terrain-following meshes, arbitrarily small cut cells are created that constraint the time-step for explicit numerical methods.

This motivates a new type of mesh that avoids arbitrarily small cells and most mesh distortions.  Combined with a new transport scheme that is formulated for stability and accuracy over steep slopes on arbitrarily-structured meshes, we alleviate numerical instabilities and inaccuracies associated with traditional transport schemes.