Abstract
Abstract : Many problems in science and engineering require the solution of a system of partial differential equations on a complex two- or three-dimensional domain. In order to solve such a problem numerically, a boundary-fitted coordinate system is usually constructed. For geometries of practical importance, it is often necessary to partition the domain and to fit a separate coordinate system to each subregion. Patching these subsystems together to form a composite system can produce irregular grid structures where the numerical scheme of solution must be modified. Methods for treating nonstandard (special) grid points in two-dimensional configurations were developed and reported earlier in the course of this project. Verification of these methods through computer experimentation and extension of the methods to special points in three-dimensional grids were the primary objectives of the project reported here. Keywords: Coordinate systems; Boundary-fitted coordinate systems; Subsystems; Two-dimensional configurations; Three-dimensional grids; Grid structures.
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