  Owing to the recent, rapid development of computer technology, the resolution
of atmospheric numerical models has increased substantially. With the use of
next-generation supercomputers, atmospheric simulations using horizontal grid
intervals of O(100) m or less will gain popularity. At such high resolution
more of the steep gradients in mountainous terrain will be resolved, which may
result in large truncation errors in those models using terrain-following
coordinates. In this study, a new 3D Cartesian coordinate non-hydrostatic
atmospheric model is developed. A cut-cell representation of topography based
on finite-volume discretization is combined with a cell-merging approach, in
which small cut-cells are merged with neighboring cells either vertically or
horizontally. In addition, a block-structured mesh-refinement technique is
introduced to achieve a variable resolution on the model grid with the finest
resolution occurring close to the terrain surface. The model successfully
reproduces a flow over a 3D bell-shaped hill that shows a good agreement with
the flow predicted by the linear theory. The ability of the model to simulate
flows over steep terrain is demonstrated using a hemisphere-shaped hill where
the maximum slope angle is resolved at 71 degrees. The advantage of a locally
refined grid around a 3D hill, with cut-cells at the terrain surface, is also
demonstrated using the hemisphere-shaped hill. The model reproduces smooth
mountain waves propagating over varying grid resolution without introducing
large errors associated with the change of mesh resolution. At the same time,
the model shows a good scalability on a locally refined grid with the use of
OpenMP.
