Numerical Simulation for Blood Flow - Microsurgery: Advances, Simulations, and Applications - page 190

be expected; the grid should be ine in these regions since the errors
are most likely to be large there. However, even an experienced
user will encounter occasional surprises and more sophisticated
methods are useful in any event. It is possible, however, to start with
a coarse grid and later reine it locally according to an estimate of
the discretization error; methods for doing this are called solution-
adaptive grid methods.
Finally, there is the issue of grid generation. When the geometry
is complex, this task usually consumes the largest amount of user
time by far; it is not unusual for a designer to spend several weeks
generating a single grid. Since the accuracy of the solution depends
as much (if not more) on the grid quality as on the approximations
used for discretization of the equations, grid optimization is a
worthwhile investment of time.
Many commercial codes for grid generation exist. The automation
of the grid generation process, aimed at reducing the user time and
speeding up the process, is the major goal in this area. Overlapping
grids are easier to generate, but there are geometries in which the
application of this approach is dificult due to the existence of too
many irregular places. The generation of triangular and tetrahedral
meshes is easier to automate, which is one of the reasons for their
popularity. One usually speciies mesh points on the bounding
surface and process from there toward the center of the domain.
When a surface grid has been created, tetrahedra is continued toward
the center of the volume along a marching front; the entire process
is something like solving an equation by a marching procedure
and, indeed, some methods are based on the solution of elliptic or
hyperbolic PDEs.
Tetrahedral cells are not desirable near walls if the boundary
layer needs to be resolved because the irst grid point must be very
close to the wall while relatively large grid sizes can be used in the
directions parallel to the wall. These requirements lead to long thin
tetrahedra, creating problems in the approximation of diffusive
luxes. For this reason, some grid generation methods generate irst
layer of prisms or hexahedra near solid boundaries, starting with a
triangular or quadrilateral discretization of the surface, on top of this
layer, a tetrahedral mesh is generated automatically in the remaining
part of the domain. An example of such a grid is shown in Fig. 5.18.