Iterative Space-Marching Method for Compressible Flows at All Speeds

Abstract

A new iterative fully coupled implicit space—marching method is proposed for solving the 2-D steady Euler equations for compressible flows at Mach numbers ranging from subsonic to supersonic. A special treatment of the streamwise pressure gradient component permits us to calculate both supersonic flow regions where the Euler equations are hyperbolic and subsonic regions where the equations reveal elliptic properties. To take into account the elliptic effects of subsonic and transonic flows space—marching sweeps are carried out iteratively. A new parabolic pressure correction procedure is developed to accelerate the convergence rate. This procedure can be applied for subsonic and transonic regimes and is consistent with the characteristic analysis of the Euler equations. At each marching station a Newton iterative technique is used to solve the nonlinear system of equations in a fully coupled manner. To resolve strong shocks and contact discontinuities as well as smooth flow fields with high accuracy implicit second—order symmetric TVD and second—order upwind Richardson schemes are employed to approximate the transverse and streamwise derivatives, respectively. Numerical calculations show that the method is accurate, robust and can efficiently be applied for calculating subsonic, transonic and supersonic flows without streamwise separation.