An efficient Newton-krylov-schur parallel solution algorithm for the steady and unsteady navier-stokes equations

We present a parallel Newton-Krylov-Schur flow solution algorithm for the threedimensional Navier-Stokes equations for both steady and unsteady flows. The algorithm employs second- A nd fourth-order summation-by-parts operators on multi-block structured grids with simultaneous approximation terms used 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 the flexible generalized minimal residual Krylov subspace iterative method with the approximate-Schur parallel preconditioner. Time-accurate solutions are evolved in time using explicit-first-stage singly-diagonally-implicit Runge-Kutta methods. The algorithm is demonstrated through the solution of the steady transonic flow over the NASA Common Research Model wing-body configuration in a range of angles of attack where substantial flow separation occurs. Several 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. Finally, the algorithm accurately captures the temporal evolution of the Taylor-Green vortex flow, highlighting the advantages of high-order spatial and temporal discretization. The algorithm presented is an efficient option for a wide range of flow problems encompassing the steady and unsteady Reynolds-averaged Navier-Stokes equations as well as large-eddy and direct numerical simulations of turbulent flows.