Advection for steep slopes and arbitrary meshes (Numerical GFD 2017)

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 constrain 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 multidimensional method-of-lines advection scheme that is formulated for stability and accuracy over steep slopes on arbitrarily-structured meshes, we alleviate numerical instabilities and inaccuracies associated with traditional advection schemes.

Presented at the workshop on numerical methods for geophysical fluid dynamics

at Imperial College London, 14th February 2017.