169 1995 Erik Sterner erik@tdb.uu.se One-dimensional Preconditioning of GMRES for the Navier-Stokes Equations Abstract The stationary Navier-Stokes equations are solved in 2D with preconditioned GMRES. The preconditioning matrix is derived from a semi-implicit Runge-Kutta scheme. The spectrum of the preconditioned coefficient matrix indicates that this approach will be successful. Numerical experiments for the flow over a semi-infinite flat plate show that the preconditioning makes GMRES converge substantially faster especially for high Reynolds numbers. The number of iterations proves to be independent of the Reynolds number.