The Generation of Three-Dimensional Body-Fitted Coordinate Systems for Viscous Flow Problems.

The proposed set of equations which generate a series of surfaces between a given inner and outer body, have been programed on CRAY-1. An extensive program testing has been carried out to make the program usable for general body shapes. For example, two methods have been developed to establish the correspondence between the points of the inner and outer surfaces, a method has been developed to find the first partial derivative of x, y, z with respect to the coordinate along the surface. All these methods are based on sound mathematical basis and have not been chosen arbitrarily. Work has been started on complicated multibody configurations, such as the wing-body combination. Here the interfacing of coordinates having sufficient derivative smoothness is the most important problem. In the period of this report, a thorough analysis on all sorts of mathematical models for coordinate generation has been completed. This analysis uncovers those differential relations which must invariably be satisfied by the metric coefficients no matter which method is used to generate the coordinates. The final computational code to be developed in the current year of effort is expected to reflect all these achievements for practical utilization.