An efficient Newton-GMRES solver for aerodynamic computations
Alberto Puyero, David W. Zingg, Alberto Puyero, David W. Zingg · 13th Computational Fluid Dynamics Conference · 1997
An efficient inexact-Newton-Krylov algorithm is presented for the computation of steady aerodynamic flows. The algorithm uses preconditioned, restarted GMRES in matrix-free form to solve the linear system arising at each Newton iteration. The preconditioner is formed using an ILU(2) factorization of an approximate Jacobian matrix after applying the Reverse Cuthill-McKee reordering. The algorithm has been successfully applied to a wide range of test cases which include inviscid, laminar, and turbulent aerodynamic flows. In all cases except one, convergence of the residual to 10~~ 12 is achieved with a CPU cost equivalent to fewer than 1200 function evaluations. The sole exception is a low Mach number case where some form of local preconditioning is needed. Several other efficient implicit solvers have been applied to the same test cases, and the matrix-free inexact-NewtonGMRES algorithm is seen to be the fastest and most robust of the methods studied. Hence this strategy is an excellent option for flow computations in which memory use is not critical, such as two-dimensional applications.