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182 6. Inviscid Flow Equations for Incompressible Flows
Linos of
equipotential
Fig. 6.1. Equipotential lines and streamlines for a source flow.
Equipotential
lines
Streamline
Fig. 6.2. Equipotential and streamlines for a potential vortex flow.
where r is the strength of the vortex. The minus sign on the right-hand side of
Eq. (6.2.11) represents a vortex with clockwise circulation.
In Section 6.4 we shall use one form of this approach (due to Hess and Smith
[1]), which is called a panel method, to solve the Laplace equation to describe
the flowfield around an airfoil at an angle of attack a.
6.3 Finite-Difference Method
To illustrate the finite-difference solution of the Laplace equation for an external
flow, consider the flow over a circular cylinder and, for convenience, use a polar
coordinate system (r, 9) rather than a Cartesian coordinate system (x,y). In
