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282 9. Grid Generation

(a) (b)

(c)
Fig. 9.13. (a) Starting algebraic C-grid around an airfoil section; 70 x 30 grid points;
inner spacing AS\ — 0.015c, outer spacing ASi = 0.3c, (b) Elliptic C-grid obtained after
smoothing the algebraic grid of (a) by the solution of Poisson equations (50 iterations),
(c) Close-up of the C-grid showing the application of orthogonality conditions near the
leading edge region.

In Appendix B we present a computer program based on the elliptic method
for generating grids.

9.6 Conformal Mapping Methods

The methods based on conformal mapping have the advantage that the transfor-
mations used are analytical or partially analytical as opposed to the differential
equation methods, which are entirely numerical. Their main drawback is their-
restriction to two-dimensional flows, since they are based on complex variables.
Nevertheless, they are very convenient for two-dimensional flows and will now
be discussed in some detail.
There are several useful meshes for airfoils, as illustrated in Fig. 9.14. The
C-mesh shown in Fig. 9.14a has high density near the leading edge of the airfoil,
and good wake resolution. The O-mesh shown in Fig. 9.14b has high density near
both the leading edge and trailing edges of the airfoil, and the H-mesh shown
in Fig. 9.14c, has two sets of mesh lines similar to the Cartesian mesh and is