A fully implicit direct Newton's method for the steady-state Navier–Stokes equations

Newton's method and banded Gaussian elimination can be a CPU efficient method for steady-state solutions to two-dimensional Navier–Stokes equations. In this paper we look at techniques that increase the radius of convergence of Newton's method, reduce the number of times the Jacobian must be factored, and simplify evaluation of the Jacobian. The driven cavity and natural convection problems are used as test problems, and finite volume discretization is employed.