Adaptive Grid Refinement for Two-Dimensional and Three-Dimensional Nonhydrostatic Atmospheric Flow

Abstract

Although atmospheric phenomena tend to be localized in both time and space, numerical models generally employ only uniform discretizations or fixed nested grids. An adaptive grid technique implemented in 2D and 3D nonhydrostatic elastic atmospheric models is described. The adaptive technique makes use of separate rectangular refinements to increase resolution where truncation error estimates are large. Multiple, rotated, overlapping grids are used along with an arbitrary number of discrete grid-refinement levels. Refinements are placed and removed automatically during the integration based an estimates of the truncation error in the evolving solution. The technique can be viewed as an extension of the nesting technique often used in atmospheric models. The adaptive model integrates the compressible, nonhydrostatic equations of motion. Although sound waves are not significant in the solution, they do constrain the time step. A splitting technique is used to accommodate the sound waves by advancing certain terms with a separate smaller time step. The terms responsible for gravity waves are also integrated with the smaller time step, and with the acoustic modes filtered through the use of divergence damping, the resulting model can be run as efficiently as hydrostatic models. Boundary conditions developed for the splitting technique in the adaptive framework are described and tested in the 2D and 3D models. The adaptive technique is shown to be efficient when compared to single fixed-grid simulations. Two new features are included in the basic solver. Also considered are additional complications that arise because of the necessary use of parameterized physics. The dependence of many parameterizations on grid scale creates difficulties in evaluating truncation error and raises more general questions concerning solution error in nested and adaptive models.