Civil Engineering Reference
In-Depth Information
(a)
(b)
Interior nodes generated
(c)
(d)
Figure 3.43
Mesh generation by the advancing-front method: (a) initial front
Γ
=
B
; (b) a new element is
pro posed on
Γ
; (c)
Γ
is updated to include the new element; (d)
Γ
= 0, mesh generation finished.
A very important concept is that at the beginning of MG, the generation front
Γ
is exactly
equal to the list of boundary segments. While the domain boundary
B
remains always the
same, the generation front
Γ
changes continuously throughout the MG process and has to be
updated from time to time whenever a new element is formed, as shown in Figure 3.43a and
b. MG terminates when there is no more line segment left in
Γ
, or
Γ
is reduced to an empty
set. The essential steps for the generation of adaptive meshes over a 2D domain in compli-
ance with a specified node spacing function are given in the following.
Step 1
:
Input the boundary segments of domain
Ω
to be meshed
The domain
Ω
is a bounded region defined by a set of line segments
B
= =
{,
i
i
1
,
N
}
B
=(, )
. In order
to deal with multi-connect regions, the internal and external boundary loops have to
be distinguished. Following the usual mathematical notations, the exterior bound-
ary will be entered in a counter-clockwise sense, whereas interior boundaries will be
entered in the clockwise sense, as shown in Figure 3.44, so that the part to be meshed
lies always on the left-hand side of a segment.
Step 2
:
Specify the node spacing function ρ over
Ω
, ρ:
Ω →
R
+
The nodal spacing ρ can be specified either explicitly by some global function covering
the entire domain
Ω
, or by adaptive meshing, in which it is given implicitly by interpo-
lation over the nodal values of a previous mesh. For the mesh of non-uniform element
size, ρ varies from point to point within
Ω
, and for any given point
x
in
Ω
, ρ(
x
) will
return a positive value as the specified element size at point
x
.
Step 3
:
Boundary discretisation
in which each line segment is connected to two nodal points, i.e.
i
PQ
i
i
A set of new nodes have to be generated along segments in
B
, such that node distribution
on the generation front complies with the given node spacing function ρ before MG.
