Quality of the Computational Grids in the Orthogonal Curvilinear Terrain-Following Coordinate and its Computational Stability

Abstract:

The orthogonal curvilinear terrain-following coordinate (OS-coordinate) proposed by Li et al. (2014) can create the orthogonal and terrain-following computational grids in the vertical, therefore reducing the advection errors compared with the corresponding non-orthogonal terrain-following grids according to the 2-D idealized Schär-type experiments. However, the orthogonal grid-lines have dramatic convergence and divergence above the steep terrain which restricts the time step and increases the numerical errors as pointed out by Li et al. (2014). In this study, we first investigate the quality of these orthogonal terrain-following grids in terms of the skewness, smoothness and aspect ratio, and their effects on reducing the advection errors. And then we design a hyperbolic rotation parameter b for the OS-coordinate instead of the power b used by Li et al. (2014) to create the new computational grids which have less convergence and divergence near the steep terrain. Finally, we use the OS-coordinate with the hyperbolic b to implement the Schär-type experiments as in Li et al. (2014) and then analyze the computational stability and the numerical accuracy relative to the OS-coordinate with the power b. The experimental results show that the hyperbolic b can control the distance of the neighbour grid-lines better than the power b, therefore alleviating the restriction of the time step in the OS-coordinate and also improving the performance of the OS-coordinate in reducing the advection errors.