A geometric interpretation of hyperbolic grid generation

Abstract

A new geometric presentation of hyperbolic grid generation has been given, and the basic concepts of hyperbolic grid generation have been extended by controlling the transverse grid are length. The new presentation is based on vector analysis, and the nonlinear equations of grid generation are obtained with the use of vector operations. The solution of the equations is based on Newton's method, and some of the iteration strategies have followed previous work in hyperbolic grid generation. A new method for generation of mesh of constant are length has been developed, and this method has been used both separately and in conjunction with orthogonal grid generation. The best results have been obtained when the are length method is combined with the orthogonal technique, and it is our opinion that this is the preferred method for future use. The arc length method can be shown to play a role similar to artificial viscosity in a rigorous way, and there is a direct tradeoff between constant arc length and orthogonality. The arc length method also gives geometrical insight into the previous use of numerical smoothing techniques, and it also increases our understanding of the use and structure of hyperbolic grid generation. The results in the paper show that the arc length method overcomes the problems that occur in hyperbolic grid generation when an initial surface with a strong concave region is encountered.