Parallel Newton–Krylov–Schur Flow Solver for the Navier–Stokes Equations

Abstract

The objective of the present paper is to demonstrate the effectiveness of a spatial discretization based on summation-by-parts operators with simultaneous approximation terms in combination with a parallel Newton–Krylov–Schur algorithm for solving the three-dimensional Reynolds-averaged Navier–Stokes equations coupled with the Spalart–Allmaras one-equation turbulence model. The algorithm employs second-order summation-by-parts operators on multiblock structured grids with simultaneous approximation terms to enforce block interface coupling and boundary conditions. The discrete equations are solved iteratively with an inexact-Newton method, while the linear system at each Newton iteration is solved using a flexible Krylov subspace iterative method with an approximate-Schur parallel preconditioner. The algorithm is verified and validated through the solution of two-dimensional model problems, highlighting the correspondence of the current algorithm with several established flow solvers. A transonic solution over the ONERA M6 wing on a mesh with 15.1 million nodes shows good agreement with experiment. Using 128 processors, the residual is reduced by 12 orders of magnitude in 86 min. The solution of transonic flow over the common research model wing–body geometry exhibits the expected grid convergence behavior. The algorithm performs well in solving flows around nonplanar geometries and flows with explicitly specified laminar-to-turbulent transition locations. Parallel scaling studies highlight the excellent scaling characteristics of the algorithm on cases with up to 6656 processors and grids with over 150 million nodes.