About grid generation in constructions bounded by the surfaces of revolution

Abstract

Abstract For constructions bounded by the surfaces of revolution, structured grid generation technique is presented. Its technology has been elaborated within the variational approach for constructing optimal grids satisfying optimality criteria: closeness of grids to uniform ones, closeness of grids to orthogonal ones and adaptation to a given function. Grid generation has been designed for numerical solution of the differential equations modeling the vortex processes of multi-component hydrodynamics. In the technology, the three-dimensional construction in which it is required to construct a grid is represented in the form of the curvilinear hexahedron defining its configuration. The specific feature of the required configurations is that some faces of a curvilinear hexahedron lie in one plane and along edges of adjoining faces grid cells degenerate into prisms. Grid generation in the considered constructions has started to be developed by the elaboration of algorithms for the volume of revolution which has become the basic construction. The basic construction is obtained by the rotation through 180? around the axis of a generatrix consisting of straight line segments, arcs of circles and ellipses. Then the deformed volumes of revolutions are considered along with the generalizations of the volume of revolution which represent constructions obtained by the surfaces of revolution with parallel axis of rotation. The aim of the further development of the technology is to consider more and more complicated constructions and elaborate the technology for them. In the presentation, the current state of the development of the technology is given. Examples of generated grids are supplied.