Numerical Simulation for Blood Flow - Microsurgery: Advances, Simulations, and Applications - page 189

5.3.3 Grid Generation
The generation of grids for complex geometries is an issue that
requires too much space to be dealt with in great detail here. We
shall present only some basic ideas and the properties that a grid
should have. More details about various methods of grid generation
can be found in topics and conference proceedings devoted to
this topic (e.g., Thompson et al ., 1985; Arcilla et al ., 1991). Even
though necessity demands that the grid be non-orthogonal, it is
important to make it as nearly orthogonal as possible. In FV methods
orthogonality of grid lines at CV vertices is unimportant — It is
the angle between the cell face surface normal vector and the line
connecting the CV centers on either side of it that matters. Thus, a
D grid made of equilateral triangles is equivalent to an orthogonal
grid, since lines connecting cell centers are orthogonal to cell
faces. Cell topology is also important. If the midpoint rule integral
approximation, linear interpolation, and central difference are used
to discretize the equations, then the accuracy will be higher if the
CVs are quadrilaterals in 2D and hexahedra in 3D, than if we use
triangles and tetrahedra, respectively. The reason is that parts of
the errors made at opposite cell faces when discretizing diffusion
terms cancel partially (if cell faces are parallel and of equal area, they
cancel completely) on quadrilateral and hexahedral CVs. To obtain
the same accuracy on triangles and tetrahedra, more sophisticated
interpolation and difference approximations must be used. Especially
near solid boundaries it is desirable to have quadrilaterals or
hexahedra, since all quantities vary substantially there and accuracy
is especially important in this region.
Accuracy is also improved if one set of grid lines closely follows
the streamlines of the low, especially for the convective terms. This
cannot be achieved if triangles and/or tetrahedra are used, but is
possible with quadrilaterals and hexahedra. Non-uniform grids
are the rule rather than exception when complex geometries are
treated. The ratio of the sizes of adjacent cells should be kept under
control, as accuracy is adversely affected if it is large. Especially
when block-structured grids are used, one should take care that the
cells are of nearly equal size near block interfaces; affector of two
variation should be the maximum. An experienced user may know
where strong variation of velocity, pressure, temperature, etc., can