From Mesh Generation


The advancing-front technique for mesh generation has been investigated for more than 35 years since the pioneering work of [A.George-1971], who studied a two-dimensional case. The classical advancing-front method, in its current form, was first described by [Lo-1985] and [Peraire et al. 1987]. Numerous improvements in this technique have been proposed over the years, first by [L hner, Parikh-1988], [Golgolab-1989] and more recently by [Mavriplis-1992] and [Shostko, L hner-1995]. This approach is now a very powerful and mature technique for generating high-quality unstructured meshes composed of simplices (triangles or tetrahedra) for domains of arbitrary shape. Variants of this technique have even been proposed to generate quadrilaterals or hexahedra in two and three dimensions (cf. [Blacker, Stephenson-1991], [Blacker, Meyers-1993]).

Classical advancing-front approaches start from a discretization of the domain boundaries as a set of edges in two dimensions or a set of triangular faces in three dimensions. The name of this class of methods refers to a strategy that consists of creating the mesh sequentially, element by element, creating new points and connecting them with previously created elements, thus marching into as yet unmeshed space and sweeping a front across the domain. The process stops when the front is empty, i.e., when the domain is entirely meshed. The front is the region(s) separating the part (or parts) of the domain already meshed from those that are still unmeshed. Hence, depending of the strategy, the front can have multiple connected components (Figure 6.1) or not (Figure 6.2).

Figure 6.1: Various...

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Mesh Generators
Mesh generators are software systems that generate a mesh in order to simulate a geometric field. They use various algorithms such as the finite element method (FEM).
Finite Element Analysis Software
Finite element analysis software (FEA) uses a numerical technique to model and analyze complex structures by solving boundary-value problems. The structure to be analyzed is divided into points (elements) that make a grid called a mesh.
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Computational fluid dynamics software (CFD) is used for the calculation of flow parameters in fluids, and for the design and simulation of the behavior of fluidic systems. CFD is also used to simulate fluid mechanics.
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Topics of Interest

Delaunay triangulation and the construction methods resulting in this triangulation have been extensive fields of research for a very long time. In particular, these topics are one of the major...

Overview Mesh generation techniques are widely employed in various engineering fields including those related to physical models described by partial differential equations (PDE). Numerical...

Mesh generation has evolved rapidly over the last decades and meshing techniques seem to have reached a level of maturity that allows them to calculate complete solutions to complex three-dimensional...

This chapter briefly discusses some mesh generation methods which do not belong to the classical methods covered in the previous chapters. The fact that there is such a wide variety of methods is some...

Overview Before going further, it seems important to clarify the terminology and to provide some basic definitions together with some notions of general interest. First, we define the covering-up of...