Higher-Order, Finite-Difference Scheme for Three-Dimensional Transonic Flowfields about Axisymmetric Bodies

Abstract

A higher-order, finite-difference scheme using a third-order shape function is applied to the three-dimensional transonic potential flow problem. Only the firstand cross-derivative terms are more accurately represented than in the conventional second-order accurate schemes. The difference equations are solved by relaxation. Both the convergence rate of the relaxation process and the accuracy for a given number of grid points are improved. The potential equation is solved under an arbitrary, locally defined coordinate transformation, capable of treating general three-dimensional geometries. Numerical results for flowfields about axisymmetric nacelles at angle of attack are presented.