Three-dimensional aerodynamic computations on unstructured grids using a Newton–Krylov approach

A Newton–Krylov algorithm is presented for the compressible Navier–Stokes equations in three dimensions on unstructured grids. The algorithm uses a preconditioned matrix-free Krylov method to solve the linear system that arises in the Newton iterations. Incomplete factorization is used as the preconditioner, based on an approximate Jacobian matrix after the reverse Cuthill–McKee reordering of the unknowns. Several approximate viscous operators that involve only the nearest neighboring terms are studied to reduce the cost of preconditioning. The performance of the algorithm is demonstrated through numerical studies of the ONERA M6 wing and the DLR-F6 wing-body configuration. A ten-order-of-magnitude residual reduction for the wing and wing-body configurations can be obtained with a computing cost equivalent to 5500 and 8000 function evaluations, respectively, on grids with a half million nodes.