Solution of the two-dimensional Euler equations with generalized coordinate transformation using flux vector splitting

Abstract

An implicit finite difference code using flux vector splitting has been developed for solving the two-dimensional inviscid gas dynamics equations. The method is spatially second-order acurate, fully conservative, and uses body-conforming generalized coordinates for treating complex geometries. Numerical results have been obtained for transonic flow over a circular cylinder and airfoils. Steady results for a half cylinder (top and bottom symmetry-imposed) range from critical flow to a strong shock case with rotationally induced flow separation. Full cylinder solutions at freestream Mach number values of 0.5, however, show unsteady oscillation. A perturbation form of the method has also been developed and used to compute both fore and aft inviscid flow separation about a cylinder for a nonuniform incoming stream.