Generation of Computational Mesh for CFPD Simulations - Computational Fluid and Particle Dynamics in the Human Respiratory System - page 79

the interpolation process. The advantages of employing such grids are that complex
domains are treated with ease and they can especially be employed to follow moving
bodies in stagnant surroundings. Some examples can be found in Tu and Fuchs
(1992) and Hubbard and Chen (1994). The disadvantages of these grids are that
conservation is usually not maintained or enforced at block boundaries, and the
interpolation process may introduce errors or convergence problems if the solution
exhibits strong variation near the interface.

4.3 Unstructured Mesh Systems

4.3.1 Unstructured Mesh Properties

Geometries encountered in the respiratory system are more likely to involve complex
geometries that do not fit exactly in Cartesian coordinates where a structure mesh
could immediately be applied. As an alternative to a body-fitted mesh, an unstruc-
tured mesh could be constructed to fill the interior of curvilinear geometries. The
unstructured mesh is most commonly comprised of triangles or tetrahedra, laid out
in an irregular pattern (Fig. 4.9 ). There are no coordinate lines that correspond to the
curvilinear directions ξ and η such as those in a body-fitted mesh, and the cells are
totally unstructured which makes the mesh highly suitable for complex geometries
such as the nasal cavity and lung airways. This means that additional computations
are needed to establish a scheme to connect neighbouring grid points. In the com-
putational programming, new data structures (e.g. edge based, face based or cell
based) are needed to store the connectivity scheme which is complicated by the fact
that a node of one cell can be connected to any number of nodes from any number
of other cells. The descriptions of some of these connectivity algorithms (Delauney,
Quadtree/Octree, and Advancing front) are briefly described in this section.

Fig. 4.9 Unstructured mesh filled with a triangular cells, b polyhedral cells, and c a hybrid mesh
combining quadrilateral cells at the wall boundaries and triangular cells in the centre

The current state of unstructured mesh CFD technology has matured, and its use
has become more prevalent with commercial CFD vendors adopting the method. In