Chapter 4 Vortex detection - Computer Graphics and Visualization

Chapter 3. Particle Tracing
3.3 Particle tracing in -transformed grids
3.3.1 -transformed grids
Point location using tetrahedral 5-decomposition regularly fails in a specific type of
grids known as -transformed grids [Sadarjoen, 1994; Sadarjoen et al., 1998a]. In our test
cases, up to 40%(!) of the particles were caught in an infinite loop between two cells, or
stopped completely. Before explaining the cause of these problems, let us first describe
this type of grids.
-transformed grids are commonly used in hydrodynamic simulations of shallow
waters, such as marine coasts or estuaries. They consist of stacked 2D xy-layers, each
of which is a well-formed quadrangular mesh with curved and approximately orthogonal
grid lines. Figure 3.4 shows an example. Corresponding nodes in different layers
have identical x,y-coordinates.
Figure 3.4: Horizontal slice of curvilinear -transformed grid of the Bay of Gdańsk (see
Section 6.2). Data courtesy WL Delft Hydraulics
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In the vertical direction, the grid lines are straight and parallel to the z-axis. -