Numbering techniques for preconditioners in iterative solvers for compressible flows

We consider Newton–Krylov methods for solving discretized compressible Euler equations. A good preconditioner in the Krylov subspace method is crucial for the efficiency of the solver. In this paper we consider a point‐block Gauss–Seidel method as preconditioner. We describe and compare renumbering strategies that aim at improving the quality of this preconditioner. A variant of reordering methods known from multigrid for convection‐dominated elliptic problems is introduced. This reordering algorithm is essentially black‐box and significantly improves the robustness and efficiency of the point‐block Gauss–Seidel preconditioner. Results of numerical experiments using the QUADFLOW solver and the PETSc library are given. Copyright © 2007 John Wiley & Sons, Ltd.