A Grid Transformation Method for a Quasi-Uniform, Circular Fine Region Using the Spring Dynamics

Abstract

　Regionally enhanced meshes that have quasi-uniformly fine circular region is proposed by a new transformation method with icosahedral grids to obtain a cost-effective simulation for waves, transports and mixing processes, the behaviors of which depend strongly on the horizontal resolution. The target region, which is designed to be composed of a finer mesh, is connected to a coarser mesh region, which is generated with the Schmidt transformation to maintain an isotropy of grid shapes. To realize these requirements, the spring dynamics method can be used and the characteristic length of the spring connecting grid nodes should be determined through three parameters; (i) the number of grid points placed in the target region, (ii) the area of the target region and (iii) a parameter of the Schmidt transformation. By introducing a set of mathematical formula, the minimum grid interval in the target region can be uniquely determined as a function of the area of the target region only. It is confirmed that fine and quasi-homogeneous meshes in the target region are generated using the grid transformation proposed in this study. Numerical simulations under realistic atmospheric conditions are performed using a non-hydrostatic model with the grid system proposed in this study and in a previous study, respectively. Because the new grid system has a more homogenous resolution in the target region compared with that of the previous study, the estimation of the momentum fluxes of gravity waves are less affected by their dependence of the grid resolution.