Nonhydrostatic Atmospheric Modeling Using a Combined Cartesian Grid

Abstract

A new method for representing topography on a Cartesian grid is applied to a two-dimensional nonhydrostatic atmospheric model to achieve highly precise simulations over steep terrain. The shaved cell method based on finite-volume discretization is used along with a cell-combining approach in which small cut cells are combined with neighboring cells either vertically or horizontally. A unique staggered arrangement of variables enables quite simple computations of momentum equations by avoiding the evaluation of surface pressure and reducing the computational cost of combining cells for the velocity variables. The method successfully reproduces flows over a wide range of slopes, including steep slopes where significant errors are observed in a model using conventional terrain-following coordinates. The advantage of horizontal cell combination on extremely steep slopes is also demonstrated.