Implicit Finite-Difference Computations of Unsteady Transonic Flows about Airfoils

A computer code, LTRAN2, has been constructed that efficiently computes low-frequency unsteady transonic flows about airfoils in motion. The code solves the two-dimensional, nonlinear, low-frequency, smalldisturbance equation by an alternating-direction implicit (ADI) algorithm. The underlying theory of the governing equation and the construction of the solution algorithm are discussed. As a check on the code, solutions computed for the linear low-frequency small-disturbance equation are compared with known answers from linear theory. Then nonlinear results are presented, and Tijdeman's experimental observations of shock wave motions resulting from airfoil flap oscillations are qualitatively reproduced computationally. These computations compare favorably with those of Magnus and Yoshihara and are obtained in substantially less computer time.