Newton solution of steady two-dimensional transonic flow

Abstract

A new method is developed for the solution of the steady, two-dimensional Euler equations for transonic flows. The discrete steady-state equations are derived in conservative finite-volume form on an intrinsic streamline grid, and are solved using Newton's method. Direct solution of the linear system of Newton equations is shown to be more efficient than iterative solution. Test cases include duct, cascade, and isolated airfoil flows, and demonstrate the speed and robustness of the method. The accuracy of the solutions is verified by comparison against values obtained analytically, experimentally and by other numerical methods.