Parallel Newton-Krylov Method for Rotary-Wing Flowfield Calculations

The use of Krylov subspace iterative methods for the implicit solution of rotary-wing flowfields on parallel computers is explored. A Newton-Krylov scheme is proposed that couples conjugate-gradient-like iterative methods within the baseline structured-grid Euler/Navier-Stokes flow solver, transonic unsteady rotor Navier-Stokes. Two Krylov methods are studied, generalized minimum residual and orthogonal s-step orthomin. Preconditioning is performed with a parallelized form of the lower-upper symmetric Gauss-Seidel operator. The scheme is implemented on the IBM SP2 multiprocessor and applied to three-dimensional computations of a rotor in forward flight. The Newton-Krylov scheme is found to be more robust and to attain a higher level of time accuracy in implicit time stepping, increasing the allowable time step. The method yields approximately a 20% reduction in solution time with the same level of accuracy in time-accurate calculations but requires more memory than do more traditional implicit techniques.