A finite difference method for the calculation of transonic flow about a wing, based on a small perturbation theory

Report (1981)

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Convergence Shock waves Swept wings Computational fluid dynamics Transonic flow Pressure distribution Finite difference theory Artificial viscosity Elliptic differential equations Non-linear equations Hyperbolic differential equations Grids Relaxation methods (mathematics) Airfoil profiles Run time (computers) Small perturbation flow

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Published Date

05-03-1981

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NLR-TR 81031 U

Abstract

A calculation method, based upon transonic small perturbation theory, is presented for the transonic flow about a semi-wing. The influence of a body can be simulated by prescribing appropriate transverse velocities in a vertical plane through the wing root. Due to the small perturbation assumption the wing should be thin and have little dihedral, camber and twist and a not too blunt leading edge. The body should be slender. The angle of incidence must be small. However, highly swept wings are allowed. A fully-conservative finite-difference scheme is implemented for a correct shock capture. Line-relaxation is used to solve the corresponding non-linear equations. A variety of numerical examples gives insight in the applicability of the method.

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