A METHOD FOR THE 2-D QUASI-ISOMETRIC REGULAR GRID GENERATION

A method for the generation of quasi-isometric boundary-fitted curvili near coordinate systems for arbitrary domains is developed on the basi s of the theory of conformal, quasi-conformal, and quasi-isometric map pings and results from the non-Euclidean geometry concerning surfaces of constant curvature, The method as it is proposed has an advantage o ver similar methods developed earlier in that the number of unknown pa rameters to be found is decreased, strict boundaries for parameters ar e found, and a simple and efficient process of identification of an un known parameter is given. The reliability of the method is assured by an existence and uniqueness theorem for quasi-isometric maps between p hysical regions and geodesic quadrangles on surfaces of constant curva ture which are used to constrict quasi-isometric grids in physical dom ains. We formulate the Riemannian metric consistent with this theorem which is available analytically. Illustrations of this technique are g iven for various domains, (C) 1998 Academic Press.