In this paper, we study an efficient strategy for constructing preconditioners for the Newton-Krylov matrix-free methods without tions on the CFL number. This results in a slow converforming explicitly the higher order matrix associated with each lingence to the steady state aerodynamic solutions. Many ear step in the Newton iteration. These preconditioners are formed authors have tried to replace explicit boundary conditions instead using an explicit derivation of a lower order matrix similar with implicit ones (see for instance [24, 18, and 10]). They to that associated with a defect-correction procedure. Comparisons showed that while high CFL number can be used, no clear of this methodology with the more standard defect-correction procedures, namely, the approximate factorization (AF) for structured advantages in terms of the CPU time as compared to exgrids and the ILU/GMRES for general grids, are then performed.
plicit boundary conditions have been drawn. This is due
To illustrate the performance of our approaches, we present some to the mismatch between the right-and left-hand side opernumerical applications to the steady solution of a two-dimensional ators. The Newton-Krylov methods in which the true
Euler flow. ᮊ 1997 Academic Press
Jacobian is computed will eliminate this mismatch. However, the derivation of the higher order Jacobian is prohibitive both in terms of the storage considerations and the * This work was supported by the National Aeronautics and Space tioner is different than that used to compute the action of Administration under NASA Contract NAS1-19480 while the author the Jacobian on a given vector (required in the Krylov was in residence at the Institute for Computer Applications in Science and Engineering. methods). The resulting methods combined with implicit 51