NEWTON-GMRES ALGORITHM APPLIED TO COMPRESSIBLE FLOWS

This paper addresses the resolution of non-linear problems arising fro m an implicit time discretization in CFD problems. We study the conver gence of the Newton-GMRES algorithm with a Jacobian approximated by a finite difference scheme and with restarting in GMRES. In our numerica l experiments we observe, as predicted by the theory, the impact of th e matrix-free approximations. A second-order scheme clearly improves t he convergence in the Newton process.