184 1996 Karl Hörnell karl@tdb.uu.se Parameter-free Krylov subspace iteration methods for the Euler and Navier-Stokes equations Abstract This paper presents a way of selecting optimal values for the CFL parameter of the Runge-Kutta method. Initial and asymptotic convergence behavior are analyzed for linear problems, with both single and multi-grid iterations, and the optimized RK is combined with other Krylov subspace methods to eliminate the fixed coefficients as well. Finally, the resulting methods are tested and evaluated for a few test cases with the real Euler and Navier-Stokes equations.