Parallel Newton-Krylov Solver for the Euler Equations Discretized Using Simultaneous-Approximation Terms

We present a parallel Newton-Krylov algorithm for solving the three-dimensional Euler equations on multiblock structured meshes. The Enter equations are discretized on each block independently using second-order-accurate summation-by-parts operators and scalar numerical dissipation. Boundary conditions are imposed and block interfaces are coupled using simultaneous-approximations terms. The summation-by-parts with simultaneous-approximation-terms approach is time-stable, requires only C-0 mesh continuity at block interfaces, accommodates arbitrary block topologies, and has low interblock-communication overhead. The resulting discrete equations are solved iteratively using an inexact-Newton method. At each Newton iteration, the linear system is solved inexactly using a Krylov-subspace iterative method, and both additive Schwarz and approximate Schur preconditioners are investigated. The algorithm is tested on the ONERA M6 wing geometry. We conclude that the approximate Schur preconditioner is an efficient alternative to the Schwarz preconditioner. Overall, the results demonstrate that the Newton-Krylov algorithm is very efficient: using 24 processors, a transonic flow on a 96-block, 1-million-node mesh requires 12 minutes for a 10-order reduction of the residual norm.