Generation of Computational Mesh for Haemodynamics Analysis - Computational Hemodynamics: Theory, Modelling and Applications - page 155

Based on the topology, mesh generation is performed as a bottom-up or top-
down approach. The bottom-up approach creates low dimensional topologies first
and builds on top higher dimensional topology, e.g. create vertices, connect these
to form edges, connect the edges to create faces, and combine the faces to create a
volume. The top-down approach creates upper dimensional topology first and uses
Boolean operations to decompose it down to lower topology.
The discretisation of the fluid equations in Chap. 5 was performed by Finite Vol-
ume and Finite Difference and Finite Element Method, which all produce a different
mesh structure. In the next section we present an introduction to mesh terminology
and different mesh designs for the fluid and structural set of equations; to assist the
reader in understanding some of the issues related with creating a usable mesh for
a haemodynamics analysis.

6.2 Mesh Configurations

6.2.1 Structured Mesh

By definition, a structured mesh is one that contains cells having either a regular-
shape element with four-nodal corner points in 2D or a hexahedral-shape element
with eight-nodal corner points in 3D. It is characterised by regular connectivity and
is a straightforward prescription of an orthogonal (90°) mesh in a Cartesian sys-
tem. This meshing should always be applied to geometries that exhibit orthogonal
shapes. Figure 6.2 shows a uniform and non-uniform structured mesh on a simple
rectangular domain in 2D and 3D. For a uniform mesh, the spacing of each cell is
a single representative value in all directions (i.e. ∆ x i = ∆ y j =∆ z k ). For non-uniformly
distributed grid points, the spacing of either ∆ x, ∆ y or ∆ z can take any values, how-
ever a prescription of a four-sided surface face is maintained. The non-uniform rect-
angular mesh in Fig. 6.2b is regarded as a “stretched” mesh where the grid points
are biased towards the wall boundaries.

6.2.2 Body-Fitted Mesh

Applying an orthogonal mesh to a non-orthogonal geometry, such as a 90 o bend in
the aortic arch, produces simplifications around the curved regions and staircase-
like steps are found (Fig. 6.3 ). Developing an approximate boundary description
around the curved edges is difficult as the steps at the boundary introduce errors
in computing the wall stress, heat flux values, and resolving the boundary layer.
Furthermore a fine mesh is required to match the curve more closely which resolves
some of the flow approximations, however this comes at a cost of high computa-
tional demands.