NEWTON METHOD APPLIED TO FINITE-DIFFERENCE APPROXIMATIONS FOR THE STEADY-STATE COMPRESSIBLE NAVIER-STOKES EQUATIONS

Newton's method is applied to finite-difference approximations for the steady-state compressible Navier-Stokes equations in two spatial dimensions. The finite-difference equations are written in generalized curvilinear coordinates and strong conservation-law form and a turbulence model is included. We compute the flow field about a lifting airfoil for subsonic and transonic conditions. We investigate both the requirements for an initial guess to insure convergence and the computational efficiency of freezing the Jacobian matrices (approximate Newton method). We consider the necessity for auxiliary methods to evaluate the temporal stability of the steady-state solutions. We demonstrate the ability of Newton's method in conjunction with a continuation method to find nonunique solutions of the finite-difference equations, i.e., three different solutions for the same flow conditions. © 1991.