Generation of quadrilateral mesh over analytical curved surfaces

Lau, T. S.; Lo, S.H.; Lee, Chi King

doi:10.1016/s0168-874x(97)00015-2

Cited by 35 publications

(18 citation statements)

References 18 publications

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“…Quadrilateral meshes may be generated from triangular meshes by merging pairs of triangles; there is a great deal of flexibility in how to do this in general, though optimising certain measures of mesh quality, and avoiding the occurrence of isolated triangles, can provide some constraints (e.g. Lau et al, 1997;Itoh and Shimada, 2002, and references therein).…”

Section: Triangles Merged Pairwise Into Quadrilateralsmentioning

confidence: 99%

Horizontal grids for global weather and climate prediction models: a review

Staniforth

Thuburn

2011

Quart J Royal Meteoro Soc

186

164

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A latitude-longitude grid is used by almost all operational atmospheric forecast models, and many research models. However, it is expected that the advantages of a latitude-longitude grid will become outweighed on massively parallel computers by data-communication bottlenecks. There is therefore renewed interest in quasiuniform alternatives. This review surveys and assesses previously proposed horizontal grids for modelling the atmosphere over the sphere. Aspects of numerical accuracy likely to be affected by grid structure are discussed; particular attention is paid to computational modes and grid imprinting. Computational modes are potentially very serious, since they may be excited in realistic applications by boundary conditions, nonlinearity, physical forcing, and data assimilation. The geometry of polyhedra is reviewed due to its relation to numerical degrees of freedom, and hence to numerical wave dispersion and the possible existence of computational modes.All grids proposed to date have known problems or issues that merit further investigation. Orthogonal logically rectangular grids may be generated using conformal maps, but these suffer from singularities and resolution clustering. Resolution clustering may be avoided by using overset grids, but there are potential issues associated with the overlap regions. Alternatively, resolution clustering may be avoided, whilst retaining a logically rectangular grid, by giving up orthogonality; however, existing numerical schemes exploit orthogonality to obtain various properties thought to be important for accuracy, and it is not yet known whether these can also be obtained on non-orthogonal grids. Quasi-uniformity and orthogonality can be obtained without resolution clustering or overlaps by using non-quadrilateral grid cells, such as triangles, or pentagons and hexagons. However, when a staggered placement of variables is used to minimise dispersion errors for fast waves, non-quadrilateral grids support computational modes.In

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Section: Triangles Merged Pairwise Into Quadrilateralsmentioning

confidence: 99%

Horizontal grids for global weather and climate prediction models: a review

Staniforth

Thuburn

2011

Quart J Royal Meteoro Soc

186

164

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“…Quadrilateral grids in general have better quality than the triangular grids. Unstructured 2D quadrilateral grids can be constructed directly by geometry decomposition [3][4][5][6], boundary advancing [7][8][9][10], and skeleton construction [11,12]; or indirectly by the background triangular grids [13][14][15][16][17]. However, the finite difference method generally uses structured quadrilateral grids (or simply called structured grids).…”

Section: S T Is Constrained By the Same Mathematical Surface Equatimentioning

confidence: 99%

Algebraic grid generation on trimmed parametric surface using non‐self‐overlapping planar Coons patch

Wang

Tang

2004

Numerical Meth Engineering

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SUMMARYUsing a Coons patch mapping to generate a structured grid in the parametric region of a trimmed surface can avoid the singularity of elliptic PDE methods when only C 1 continuous boundary is given; the error of converting generic parametric C 1 boundary curves into a specified representation form is also avoided. However, overlap may happen on some portions of the algebraically generated grid when a linear or naïve cubic blending function is used in the mapping; this severely limits its usage in most of engineering and scientific applications where a grid system of non-self-overlapping is strictly required. To solve the problem, non-trivial blending functions in a Coons patch mapping should be determined adaptively by the given boundary so that self-overlapping can be averted. We address the adaptive determination problem by a functional optimization method. The governing equation of the optimization is derived by adding a virtual dimension in the parametric space of the given trimmed surface. Both one-and two-parameter blending functions are studied. To resolve the difficulty of guessing good initial blending functions for the conjugate gradient method used, a progressive optimization algorithm is then proposed which has been shown to be very effective in a variety of practical examples. Also, an extension is added to the objective function to control the element shape. Finally, experiment results are shown to illustrate the usefulness and effectiveness of the presented method.

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“…Rank et al [8] proposed a technique to transform triangular meshes into quadrilateral meshes by splitting two neighbouring triangles. Lee et al [9,10] later extended their work to generate full quadrilateral meshes by introducing the systemic merging technique (SMT). By combining the SMT with techniques used in the paving algorithm, Owen et al [11] developed the Q-MORPH algorithm for planar and surface quadrilateral mesh generations.…”

Section: Introductionmentioning

confidence: 99%

A new indirect anisotropic quadrilateral mesh generation scheme with enhanced local mesh smoothing procedures

Lee

2003

Numerical Meth Engineering

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SUMMARYAn enhanced version of indirect advancing front technique is proposed for the construction of full quadrilateral anisotropic meshes on 3D surfaces. The ÿnal quadrilateral mesh is constructed from a background triangular mesh and the merging procedure is carried out in the parametric space. The proposed method employed the systemic merging technique for the formation of quadrilaterals and the metric speciÿcations for controlling the anisotropic characteristics of the elements. In order to generate well-graded anisotropic quadrilaterals, the selection criteria of base segment for merging are carefully deÿned. Furthermore, in order to improve the shape quality of the ÿnal mesh, a set of new local smoothing algorithms for anisotropic quadrilateral mesh quality enhancement has been proposed and tested in this study. Numerical examples obtained indicate that the proposed enhanced local smoothing schemes can e ectively improve the quality of the quadrilateral meshes produced and increase the robustness of the mesh generation scheme.

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Generation of quadrilateral mesh over analytical curved surfaces

Cited by 35 publications

References 18 publications

Horizontal grids for global weather and climate prediction models: a review

Horizontal grids for global weather and climate prediction models: a review

Algebraic grid generation on trimmed parametric surface using non‐self‐overlapping planar Coons patch

A new indirect anisotropic quadrilateral mesh generation scheme with enhanced local mesh smoothing procedures

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