A parallel Newton-Krylov-Schur flow solver for the Navier-Stokes equations using the SBP-SAT approach

This paper presents a three-dimensional Newton-Krylov flow solver for the NavierStokes equations which uses summation-by-parts (SBP) operators on multi-block structured grids. Simultaneous approximation terms (SAT’s) are used to enforce the boundary conditions and the coupling of block interfaces. The discrete equations are solved iteratively with an inexact Newton method. The linear system of each Newton iteration is solved using a Krylov subspace iterative method with an approximate-Schur parallel preconditioner. The algorithm is validated against an established two-dimensional flow solver. Additionally, results are presented for laminar flow around the ONERA M6 wing, as well as low Reynolds number flow around a sphere. Using 384 processors, the solver is capable of obtaining the steady-state solution (reducing the flow residual by 12 orders of magnitude) on a 4.1 million node grid around the ONERA M6 wing in 4.2 minutes. Convergence to 3 significant figures in force coefficients is achieved in 83 seconds. Parallel scaling tests show that the algorithm scales well with the number of processors used. The results show that the SBP-SAT discretization, solved with the parallel Newton-Krylov-Schur algorithm, is an efficient option for three-dimensional Navier-Stokes solutions, with the SAT’s providing several advantages in enforcing boundary conditions and block coupling.