Surface grid generation in the tangent plane
type: Item
instance of: scholarly article
title: Surface grid generation in the tangent plane
zbMATH Open document ID: 0831.65122
DOI: 10.1016/S0096-3003(93)90040-L
author: Patrick M. Knupp
published in: Applied Mathematics and Computation
publication date: 1996-02-18T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65N50
zbMATH DE Number: 519643
zbMATH Keywords: surface tangent plane
zbMATH Keywords: numerical experiments
zbMATH Keywords: surface grid generation algorithms
zbMATH Keywords: bifurcation
zbMATH Keywords: truncation error
reviewed by: Helmut Weber
MaRDI profile type: Publication
cites work: Variational grid generation
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cites work: Q5332396
cites work: Q5802681
cites work: Anomalies in grid generation on curves
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cites work: Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary two-dimensional bodies
Wikidata QID: Q127899157
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description: scientific article; zbMATH DE number 519643