Developments of the Orthogonal Curvilinear Terrain-Following Coordinate: the New Basis Vectors

We have developed the orthogonal curvilinear terrain-following coordinate (OS-coordinate) proposed by Li et al. (2014), especially focusing on the restriction of the time step in the OS-coordinate. We first propose two new methods to solve the basis vectors of the OS-coordinate, both of which avoid the spatial rotation proposed by Li et al. (2014), therefore simplifying the solving procedure of the OS-coordinate. Moreover, for the major drawback of the OS-coordinate, which is the convergence and the divergence of the grid-lines pointed out by Li et al. (2014), we revise their basis vectors and design a new general rotation parameter to create the new basis vectors of the OS-coordinate. The experimental results show that using these new basis vectors, we can improve the orthogonality of the 3-D coordinate surfaces of the OS-coordinate. More importantly, we can easily control the distance between the neighbour grid-lines, therefore alleviating the restriction of the time step in the OS-coordinate. These have been validated by the idealized Schär-type advection experiments.