A matrix-free preconditioned Newton/GMRES method for unsteady Navier–Stokes solutions
✍ Scribed by Ning Qin; David K. Ludlow; Scott T. Shaw
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 287 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0271-2091
No coin nor oath required. For personal study only.
✦ Synopsis
The unsteady compressible Reynolds-averaged Navier -Stokes equations are discretized using the Osher approximate Riemann solver with fully implicit time stepping. The resulting non-linear system at each time step is solved iteratively using a Newton/GMRES method. In the solution process, the Jacobian matrix-vector products are replaced by directional derivatives so that the evaluation and storage of the Jacobian matrix is removed from the procedure. An effective matrix-free preconditioner is proposed to fully avoid matrix storage. Convergence rates, computational costs and computer memory requirements of the present method are compared with those of a matrix Newton/GMRES method, a four stage Runge-Kutta explicit method, and an approximate factorization sub-iteration method. Effects of convergence tolerances for the GMRES linear solver on the convergence and the efficiency of the Newton iteration for the non-linear system at each time step are analysed for both matrix-free and matrix methods. Differences in the performance of the matrix-free method for laminar and turbulent flows are highlighted and analysed. Unsteady turbulent Navier -Stokes solutions of pitching and combined translation-pitching aerofoil oscillations are presented for unsteady shock-induced separation problems associated with the rotor blade flows of forward flying helicopters.