Steady three-dimensional turbulent flow computations with a parallel Newton-Krylov-Schur algorithm

Abstract

We present computations of steady three-dimensional turbulent flows with a parallel Newton-Krylov-Schur solution algorithm. The algorithm solves the Reynolds-Averaged Navier-Stokes equations coupled with the Spalart-Allmaras one-equation turbulence model, with the optional use of quadratic constitutive relations. The governing equations are discretized on multi-block structured grids using summation-by-parts operators with simultaneous approximation terms to enforce boundary and block interface conditions. We present a discussion on algorithm performance metrics, including speed, accuracy, and efficiency, and suggest several metrics which can be used for algorithm comparisons, such as convergence time, equivalent right-hand-side evaluations, computing time per grid node, and time required to reach specific functional error levels as compared to grid-converged values. The suggested metrics are applied to the current algorithm in the solution of subsonic and transonic flows around the ONERA M6 and NASA Common Research Model geometries. The results show effective algorithm convergence as grid resolution is increased, converging the residual by 12 orders of magnitude for all cases. A third geometry, based on the 1st AIAA High Lift Prediction Workshop delta wing configuration, provides difficulty in obtaining full convergence, leveling the residual off at a reduction of 4 to 5 orders of magnitude. However, the partially converged solutions show excellent agreement of lift and drag coefficients with experimental data in the angle of attack range of 1 to 40.