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accuracy accurate advantage airfoil problem analysis analyzed approximate mapping arbitrary airfoil Argyris assumed asymptotic patching asymptotic solution automated automatic mesh boundary conditions calculated cascade problem chapter circle circular cylinder circumferential coefficient compressible flow Conditions and Constraints contour integral convergence coordinate system cylindrical coordinates density doublet element influence matrix error evaluation exact solution Figure finite differences finite element method flow problems formulated free flow geometry global influence matrix global variational principle governing equation irrotationality condition iterative variational integral Joukowski transformation kinetic energy Kutta condition Laplace equation Laplace's linear mesh distribution minimizing Multibody Problems nodal points nodal values nonlinear number of iterations obtain outer boundary outer contour patching approach perturbation potential flow present pressure distribution procedure pseudocircle r-l r-l radial mesh radius region single airfoil singularities solve stagnation point streamfunction subsonic supersonic transonic unbounded flow uniform flow variational principle velocity distribution velocity potential vhere wind tunnel