Application of continuous dynamic grid adaptation techniques to meteorological modeling. Part I: basic formulation and accuracy

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 and stationary distribution of grid points. The distribution of grid points is found by the solution of "grid-generator' equations which in turn can be derived as a weighted combination of several variational problems, each of which attempts to enforce a particular desirable property of the grid. These properties include the smoothness and orthogonality of the grid point distribution and its response to the user-defined "weight function', which is a quantitative measure of where the local resolution is to be increased. -from Authors