A Simple Adaptive Grid Method in Two Dimensions

This paper gives an interpretation of the concept of equidistribution in the context of adaptive grid generation for multidimensional problems. It is shown that the equidistribution principle cannot be satisfied throughout the domain of the problem and, based on this recognition, a local equidistribution principle is developed. A discrete formulation is described for grid generation in two space dimensions and a smoothing mechanism is presented for improving mesh quality. The adaptive grid method that is constructed contains three grid-quality parameters. Numerical examples illustrate adaptive grid generation using a prescribed monitor function and grid generation for numerical solution of partial differential equations. Results show that the method produces high quality grids and that it is fairly insensitive to the choice of parameters.