Numerical generation of three-dimensional coordinates between bodies of arbitrary shapes

Abstract

Abstract : This paper is devoted to the numerical solution of a set of second order elliptic partial differential equations for the generation of three-dimensional curvilinear coordinates between two arbitrary shaped bodies. The central idea of the method is to generate a series of surfaces between the given inner and the outer boundary surfaces and then to connect these surfaces in such a manner so as to have a sufficiently differentiable three-dimensional coordinate net in the enclosed region. It is important to state here that the proposed equations for the numerical solution form a consistent set of second order elliptic equations which are a consequence of the equations of Gauss for a surface. Additional constraints are then imposed which, besides yielding the simplest form of equations for numerical purposes, also preserve the essential geometric properties of the generated surfaces. (Author)