21st Congress of International Council of the Aeronautical Sciences, Melbourne, Australia, 13-18 September, 1998
Paper ICAS-98-7.4.1

IMPROVED APPROXIMATE FACTORISATION ALGORITHM FOR THE STEADY SUBSONIC AND TRANSONIC FLOW OVER AN AIRCRAFT WING

Ly E.
Royal Melbourne Institute of Technology, Australia

Keywords: factorisation algorithm, steady subsonic, transonic flow, aircraft wing

This paper describes an approximate factorisation (AF) algorithm, for the solution of the two-dimensional steady Subsonic Small Disturbance (SSD) Equation. The algorithm employs internal Newton iterations, at each time level, to achieve time accuracy and computational efficiency. For steady flow computations, an "artificial" time dependent derivative term is introduced into the SSD Equation to incorporate temporal numerical dissipation. This term is implemented for variable time stepping, to allow for step size cycling to accelerate convergence to 'steady-state. In the AF algorithm, the reduced potential is determined via an iterated finite difference scheme, in which the coefficient matrix acting on the unknown reduced potential difference is approximately factored. The reduced potential is then determined via the solution of two tri-diagonal linear systems. The size of the time step is cycled in a predetermined fashion, with the minimum and maximum time steps based on the spatial grid spacing. Results for steady subsonic flow over an aerofoil, with a 10% thick double parabolic arc profile, inclined at 0° and 1° angle of attack (AOA) are presented. To demonstrate that the method works for nonlinear partial differential equations, results for three-dimensional steady subsonic and transonic flow over a F5 wing are presented.

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