Numerical advection over steep terrain

There are many ways to represent terrain in atmospheric models. Terrain following coordinates are in widespread operational use but can suffer from numerical errors near steep slopes. The cut cell method can alleviate such errors but arbitrarily small cut cells severely constrain the timestep when explicit methods are used.

We present a new type of mesh, the slanted cell mesh, which avoids severe timestep constraints by creating cells that are long in the direction of flow. We also present a new finite volume advection scheme that is suitable for arbitrary meshes. The scheme uses a new stabilisation technique to improve advection accuracy near steep terrain without increasing the computational cost during integration.

The slanted cell mesh and the new advection scheme are assessed in a newly formulated test case which challenges schemes at the lower boundary. We show that the new advection scheme is resilient to mesh distortions and misalignment of the flow with the mesh.