ABSTRACT
The necessity to maintain coordinate lines coincident with the boundaries must be mentioned. A significant simplification in coding, most particularly with regard to boundary conditions, can be attained in constructing the grid operator. A concentration of lines in regions of high gradients is desirable and can increase accuracy of the method. Transformation for stationary problems or nonstationary problems approximated by implicit schemes, the use of grids of the mentioned type can result in the very favorable possibility to apply effective methods for solving the arising systems. Conformal mappings using elementary transformations in the complex plane have long been used to generate orthogonal coordinate systems about special boundary curves that are contours of the mapping. Many numerical procedures have been designed to produce coordinates that are nearly orthogonal. For generation of nonorthogonal coordinate systems and corresponding grids, several types of elliptic generating systems can be mentioned, including a certain class of quasilinear equations.
