Surface grid generation in the tangent plane

摘要

Recent work has shown that parametrically formulated surface grid generation algorithms are severely limited by solution bifurcations of the discretized equations. Such bifurcations become apparent if the given surface has points of high curvature. The present study demonstrates that discrete equations derived from an alternative physical variables formulation do not result in similar bifurcations. However, the natural formulation using physical variables is not entirely successful on surface of high curvature due to excessive truncation error in the solution grid. It is shown that both bifurcations and truncation error are overcome by formulating the grid generation equations in terms of projections of the physical variables onto the surface tangent plane.