A rather common discretisation with numerical models of the atmosphere is the terrain following grid, where lines of grid points follow the mountains. While this method is accurate with very smooth mountains (mountains which are supported by many grid points), in cases with realistic mountains large errors are encountered [see 1]. Such errors can be avoided by using lines of grid points which are horizontal and consequently cut into the mountains.
A test for the cut the cut cells discretisation is the advection along a smooth mountain surface. For this test it requires some consideration to obtain reasonable and smooth solutions [2]. For some prediction schemes false boundary conditions are posed, which for fast waves would be OK, but are not allowed with the advection equation. Therefore for such false approximations wrong solutions which are very noisy at the mountain surface are produced. A very smooth surface of a mountain is obtained when the mountain is a straight line. Fig 1 gives an example of smooth advection along such a straight line mountain which is free of the mentioned noise and convergence problems:
Fig 1: left: Cut cells with the straight mountain test and the sparse o3o3 method. The initial and predicted fields are shown for a movement along the straight mountain (for sparse features of this figure see [1]. Right: the advection of a density field away from the straight mountain.
The advection along a line diagonal to the square area implies a rather regular grid [1]. For any other direction the mountain will cut small and large triangular and pentagonal cells out of a square grid. This leads to difficulties for the numerical treatment [1].
The reader with more serious interest in cut cells will need some knowledge in the programming language Fortran and the operating system Unix/Linux. A login to an account on our server will be necessary.