A generalized scheme for three-dimensional hyperbolic grid generation

Abstract

A hyperbolic grid generation scheme formulated from grid orthogonality and cell volume specification is generalized such that high quality three-dimensional grids can be obtained for a wide variety of geometries. The speed of the scheme is one to two orders of magnitude faster than typical elliptic grid generation methods. The robustness of the scheme is significantly enhanced by several new techniques. By using a spatially variable smoothing coefficient, orthogonality and smoothness of the grid are maintained around complex concave and convex surface topologies. A metric correction procedure is employed to guarantee that the grid marches out of a corner by bisecting the angles subtended by the neighboring points. Extra robustness at severe convex corners is achieved by special local treatments. Different extrapolation methods are used to provide smoothness at floating edges and axis regions. The versatility of the new hyperbolic grid generation scheme is demonstrated by three-dimensional grids generated for external components of the intergrated Space Shuttle vehicle and the SOFIA telescope.