A parallel Newton-Krylov flow solver for the Euler equations on multi-block grids

Abstract

We present a parallel Newton-Krylov algorithm for solving the three-dimensional Euler equations on multi-block structured meshes. The Euler 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 approximation terms (SATs). 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 considered. The algorithm is tested on the ONERA M6 wing. The results show that a discretization based on SATs is well suited to a parallel Newton-Krylov solution strategy, and that the approximate Schur preconditioner is more efficient than the Schwarz preconditioner in terms of CPU time and Krylov iterations, for both flow and adjoint solves.