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

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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... 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...

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