Preconditioning Techniques for the Newton-Krylov Solution of Compressible Flows

In this paper, we study an efficient strategy for constructing preconditioners for the NewtonÂ?Krylov matrix-free methods without forming explicitly the higher order matrix associated with each linear step in the Newton iteration. These preconditioners are formed instead using an explicit derivation of a lower order matrix similar to that associated with a defect-correction procedure. Comparisons of this methodology with the more standard defect-correction procedures, namely, the approximate factorization (AF) for structured grids and the ILU/GMRES for general grids, are then performed. To illustrate the performance of our approaches, we present some numerical applications to the steady solution of a two-dimensional Euler flow.

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