Krylov Methods for Compressible Flows

In this paper we investigate the application of Krylov methods to compressible ows, and the e ect of implicit boundary conditions on the implicit solution of nonlinear problems. Two defect-correction procedures, namely, Approximate Factorization (AF) for structured grids, and ILU/GMRES for general grids are considered. Also, considered here, is Newton-Krylov matrix-free methods that we combine with the use of mixed discretization schemes in the implicitly de ned Jacobian and its preconditioner. Numerical experiments that show the performance of our approaches are then presented. This work was supported by the National Aeronautics and Space Administration under NASA contract NAS1-19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA 236810001.