Application of Continuous Dynamic Grid Adaption Techniques to Meteorological Modeling. Part I: Basic Formulation and Accuracy

Abstract

Abstract The continuous dynamic grid adaption (CDGA) technique developed in astrophysics and aeronautics is applied, to our knowledge, for the first time to meteorological modeling. The aim of CDGA is to improve the accuracy of numerical solutions of partial differential equations (typically those governing fluid flow) by the use of nonuniform grids that have higher local resolution in regions where the numerical error is presumed to be large. Conceptually, CDGA has some relationship to the well-known technique of grid stretching, but its power lies in its ability to determine an appropriate spatial distribution of grid points automatically and to update this distribution in response to changes in the evolving numerical solution. Application of the technique is facilitated by transforming the governing equations from physical space in which the grid is nonuniform, nonorthogonal and for which the individual grid points are in continuous motion to computational space, which by definition has both a regular ...