Page 96 - Basics of Fluid Mechanics and Introduction to Computational Fluid Dynamics

Dynamics of Inviscid Fluids 81

To the above abscissa z) it is possible to join the corresponding or-
dinate y), either from the given tabular or from the functional form,
and then we can also obtain the coefficients R@ — po, py), gs? which
will be calculated via the mentioned integral relations. Using these coef-

ficients new abscissas and then new ordinates are calculated and so the
process is continued. For instance, within the iteration of m order (m-th
iteration) we have

o(™-1) (0) = a+fcos 0+q6")) sin 6+5— ( (m—}) cos n6 + qin?) sin n®)
n=2

27
(6) sin
rf” +R =p, RO — p™) = 1 / y™) 048,

0
from where

B 1 20
R (my —~F 4 oc Jy alm) (9) sin 0d0.
at
|
0
The iterative method sketched above is easy to use on a computer.
The only additional required subprograms are connected to the interpo-
lation such that in each “sweep” new values of the ordinates, respectively

abscissas, become available. The method converges quite fast.

6. Panel Methods for Incompressible Flow of
Inviscid Fluid

The panel methods in both source and vortex variants, are numerical
methods to approach the incompressible inviscid fluid flow, and which,
since the late 1960s, have become standard tools in the aerospace indus-
try. Even if in the literature the panel methods occur within “computa-
tional aeronautics’, we will consider them as a method of CFD.
In this section we will “sketch” the panel method, separately in the

source variant and then in the vortex variant, by considering only the
“first order” approximation.

6.1 The Source Panel Method for Non-Lifting
Flows Over Arbitrary Two-Dimensional

Bodies
Let us consider a given body (profile) of arbitrary shape in an incom-

pressible inviscid fluid flow with free-stream velocity V,,. Let a contin-