Elliptic grid generation with orthogonality and spacing control on an arbitrary number of boundaries
A procedure for the generation of two and quasi-three-dimensional grids with control of orthogonality and spacing with respect to any and/or all boundaries of the domain is described. The elliptic grid generation equations of Thompson are solved implicitly. Control of the grid behavior is achieved through the introduction of forcing functions terms in the manner of Steger and Sorenson or in a modification of the method of Hilgenstock. The forcing function terms are constructed on the boundaries and propagated into the domain using transfinite Lagrangian bivariate interpolation. An anisotropic transfinite stencil is introduced and is shown to produce excellent grid behavior particularly in the vicinity of corner singularities. Emphasis is placed on the generation of viscous grids and the method is shown to be suited for use in the generation of grids for internal as well as external flow geometries. A FORTRAN program named PISCES has been written to implement the algorithm. Examples of grids for internal and external flows are given that highlight the characteristics and behavior of the algorithm.