Surface grid generation in the tangent plane
Recent work of \textit{S. Steinberg} and \textit{P. J. Roache} [Numer. Methods Partial Differ. Equations 2, 71-96 (1986; Zbl 0623.65127)] has shown that parametric surface grid generation algorithms are severely limited by the bifurcation of solutions of the discretized equations. This becomes apparent if the given surface has points of high curvature. Bifurcations could not be avoided by alternate difference schemes or by increased grid resolutions. The present paper shows that discrete equations derived from a formulation using alternative physical variables do not result in similar bifurcations. However it is not entirely successful on surfaces of high curvature due to the truncation error in the solution grid. The author shows that both bifurcation and truncation error are overcome by formulating the grid generation equations in terms of projections of the physical variables onto the tangent plane of the surface. Numerical experiments suggest that the discrete tangent plane equations are not subject to either bifurcations or too large truncation errors. Some questions require further research, for example, why does the parametric, but not the physical variables approach lead to bifurcation.
scientific article; zbMATH DE number 519643
scientific article