On some integral equation methods in two-dimensional transonic flow

The linear flow field horizontal velocities around various airfoils have been obtained analytically and are compared with the velocities calculated using the exponential and inverse square functional relationships between horizontal surface velocity and the vertical coordinate. It is found that the velocities, obtained by using the two different functional relations, match closely with the analytical solution except near the leading edge and trailing edge.

Further, subcritical and supercritical flows over 6 percent biconvex and NACA 0012 airfoils at zero incidence have been obtained using the standard integral equation method but with a better approximate starting solution for the iteration scheme. It is found that this approach makes the solution converge much faster than the existing methods. Gauss Legendre quadrature method has been also used to solve the integral equation for subcritical flows. It is observed that this method is not efficient as far as computing time is concerned.