Implicit finite-difference computations of unsteady transonic flows about airfoils, including the treatment of irregular shock-wave motions

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, small-disturbance equation by an alternating-direction implicit (ADI) algorithm. First, as a check on the code, LTRAN2 is used to solve the linear, low-frequency, small-disturbance equation. The results are compared with known answers from linear theory. Then nonlinear results are presented. Tijdeman's experimental observations of shock wave motions resulting from airfoil flap oscillations are qualitatively reproduced by LTRAN2. These computations compare favorably with those of Magnus and Yoshihara and are obtained in substantially less computer time. Also the underlying theory of the governing equation and the construction of the algorithm are discussed.