Environmental Engineering Reference
In-Depth Information
boundary-fitted grid approach (Fig. 12.2b) (Liang
et al. 2007a) combines this with the advantage
of geometric flexibility, but grid generation for
applications to highly irregular geometries is dif-
ficult. The alternative of using square-structured
grids is still overwhelmingly popular because of its
simplicity. Therefore, recent research efforts have
concentrated on the development of methods that
treat variability in the physical domain and in
the topography at the sub-cell level. For example,
the Cartesian cut cell method uses a background
Cartesian grid for themajority of the flow domain,
with special treatments being applied to cells that
are cut by solid bodies. The development of the
method is described in Ingram et al. (2003), and a
recent application to inundation modelling is pro-
posed in Morris et al. (2006). A different approach
relying on the so-called quadtree grid generation
methodology (Fig. 12.8) has been promoted in
recent years (Liang et al. 2008; Liang and
Borthwick 2009). Quadtree grids are structured
square grids that can be locally refined according
to criteria associated, for example, to transient
hydrodynamic properties of the flow or to spatial
topographic variability. Their main feature is that
local refinement is only carried out through a
recursive spatial decomposition process where a
square cell can only be subdivided into four smal-
ler and also square cells. This allows the use of
Unstructured grid-models are seen by many as
the most promising way forward (Namin et al.
2004; Begnudelli and Sanders 2006; Hervouet
2007), because of their potential for non-uniform
grid resolution, allowing refinement only where
needed and thereby saving computational effort.
However, automatic grid generation techniques
for unstructured grids are at an early stage of
development for applications in flood flowmodel-
ling. Most commercial unstructured-grid models
still require time-consuming human intervention
(Sauvaget et al. 2000). However, significant ad-
vances in the field (see, e.g., Shewchuk 1996;
Owen and Shephard 2003) are beginning to be
applied (e.g. Begnudelli and Sanders 2006), includ-
ing in some commercially available software (e.g.
Infoworks-RS 2D; see Gutierrez-Andres et al.
2008). 'Smart' grid generation techniques that are
specifically designed for floodplain flow model-
ling, and that integrate physical features of the
floodplains digitized in the form of breaklines (see
Fig. 12.5) or building outline polygons are being
implemented. It is also worth mentioning
research algorithms that make mesh resolution
locally dependent on vegetation features (e.g.
Cobby et al. 2003). Such advances are, however,
still to be used in engineering practice.
Advantages of structured grids over unstruc-
tured grids include algorithmic simplicity. The
Fig. 12.8
Quadtree grid
modelling. From Liang
et al. (2008).
