Chapter 4 Vortex detection - Computer Graphics and Visualization

3.2 Particle tracing in curvilinear grids
3.2.1 Curvilinear grids
3.2. Particle tracing in curvilinear grids
In practice, many CFD applications do not use uniform grids, but structured curvilinear
grids, consisting of deformed, hexahedral cells, with curved faces (see also Section 2.1).
An advantage of curvilinear grids is their ability to conform to the shape of curved
or complex geometries, such as airplane wings and coast lines. Another advantage
is their regular topological structure, so the cells and data are addressable through indices
( . A disadvantage of these grids is that algorithms working in them become
more complex, because the cells are no longer cubes. Figure 3.1 shows an example of a
curvilinear grid. More information about this grid and the corresponding data set are
given in Section 3.5.1.
Figure 3.1: Curvilinear grid of a 3D Backward-Facing Step (see Section 3.5.1)
A strategy often applied in many CFD simulation systems works by transforming
the curvilinear grid to a uniform rectilinear grid in a new domain. The grid and data,
which are typically specified in the ‘normal’ domain called physical space, or P-space,
are then transformed to a new domain called computational space, or-space. The integration
steps are done in -space, and the resulting positions are transformed back
to È-space. Unfortunately, for particle tracing algorithms, this method often leads to
23