Applied Computational Fluid Dynamics Techniques - Wiley Episode 1 Part 3 pptx

36 APPLIED COMPUTATIONAL FLUID DYNAMICS TECHNIQUES

Conforming

Surface aligned

Non-conforming

Non-surface aligned

Micro-structured - Micro-unstructured Macro-unstructured

Element type

Micro-structured

Figure 3.1. Characterization of different mesh types

Element type describes the polyhedron used to discretize space. Typical element types

include triangles and quads for 2-D domains, and tetrahedra, prisms and bricks for 3-D

domains.

In principle, any of the four classifications can be combined randomly, resulting in a very

large number of possible grid types. However, most of these combinations prove worthless.

As an example, consider an unstructured grid of tetrahedra that is not body conforming. There

may be some cases where this grid optimally solves a problem, but in most cases Cartesian

hexahedral cells will lead to a much faster solver and a better suited solution. At present, the

main contenders for generality and ease of use in CFD are as follows.

(a) Multiblock grids. These are conformal, surface-aligned, macro-unstructured, micro

structured grids consisting of quads or bricks. The boundaries between the individual

micro-structured grids can either be conforming or non-conforming. The latter class

of multiblock grids includes the possibility of overlapped micro-structured grids, also

known as Chimera grids (Benek et al. (1985), Meakin and Suhs (1989), Dougherty and

Kuan (1989)).

(b) Adaptive Cartesian grids. These are non-conformal, non-surface-aligned, micro￾unstructured grids consisting of quads or bricks. The geometry is simply placed into

GRID GENERATION 37

an initial coarse Cartesian grid that is refined further until a proper resolution of the

geometry is achieved (Melton et al. (1993), Aftosmis et al. (2000)). The imposition of

proper boundary conditions at the edges or faces that intersect the boundary is left to

the field solver.

(c) Unstructured uni-element grids. These are conformal, surface-aligned, micro￾unstructured grids consisting of triangles or tetrahedra.

Consider the task of generating an arbitrary mesh in a given computational domain. The

information required to perform this task is:

(a) a description of the bounding surfaces of the domain to be discretized;

(b) a description of the desired element size, shape and orientation in space;

(c) the choice of element type; and

(d) the choice of a suitable method to achieve the generation of the desired mesh.

Historically, the work progressed in the opposite order to the list given above. This is not

surprising, as the same happened when solvers were being developed. In the same way that

the need for grid generation only emerged after field solvers were sufficiently efficient and

versatile, surface definition and the specification of element size and shape only became

issues once sufficiently versatile grid generators were available.

3.1. Description of the domain to be gridded

There are two possible ways of describing the surface of a computational domain:

(a) using analytical functions; and

(b) via discrete data.

3.1.1. ANALYTICAL FUNCTIONS

This is the preferred choice if a CAD-CAM database exists for the description of the domain,

and has been used almost exclusively to date. Splines, B-splines, non-uniform rational B￾splines (NURBS) surfaces (Farin (1990)) or other types of functions are used to define

the surface of the domain. An important characteristic of this approach is that the surface

is continuous, i.e. there are no ‘holes’ in the information. While generating elements on

the surface, the desired element size and shape is taken into consideration via mappings

(Löhner and Parikh (1988b), Lo (1988), Peiro et al. (1989), Nakahashi and Sharov (1995),

Woan (1995)).

3.1.2. DISCRETE DATA

Here, instead of functions, a cloud of points or an already existing surface triangulation

describes the surface of the computational domain. This choice may be attractive when no

CAD-CAM database exists. Examples are remote sensing data, medical imaging data, data