The numerical solution of two-dimensional fluid flow problems

A numerical solution method is developed for the solution of two-dimensional, irrotational and compressible fluid flow problems. The partial differential equation, in terms of the velocity potential, describing the flow is replaced by finite difference equations and the resulting matrix is solved by Gaussian elimination. The method is successfully applied to two subsonic flow problems: a 7.5⁰ wedge and a 6⁰ wedge inlet. The method becomes invalid, as expected, with the appearance of sonic velocity in the flow field. An investigation of the definition of the singularities is made. This indicates that the best agreement with the experimental results for the same problem is obtained when the flow directions at the singularities are assumed to be equal to that of the wedge. Methods are postulated to remove the restraints associated with a limited field size by replacing the boundary values, after the initial solution, with values extrapolated from the flow field --Abstract, page ii