Abstract:
Methods are given in this paper of dealing with singularities of functions satisfying certain two dimensional partial differential equations. For a numerical solution the differential equations are replaced by difference equations on a square mesh. Log (I/q) where q is the Velocity, becomes infinite at stagnation points, sharp corners, sinks, etc., while the conjugate function 0 (flow direction) becomes multi-valued. The method consists in finding a series expansion for the function (log 1/q or 0) in the neighbourhood of the singularity. This expansion is then used to find relationships between the function values at points of the mesh adjacent to the singularity. A method of working directly in the transformed flow plane (in which the aerofoil is a slit), and thus avoiding irregular squares on the boundary, is also given. The method is developed for incompressible flow, but an approximation suitable for compressible flow is given.
