Newton–Krylov Algorithm with a Loosely Coupled Turbulence Model for Aerodynamic Flows

A fast Newton–Krylov algorithm is presented that solves the turbulent Navier–Stokes equations on unstructured 2-D grids. Themodel of Spalart andAllmaras provides the turbulent viscosity and is loosely coupled to themean-flow equations. It is often assumed that the turbulence model must be fully coupled to obtain the full benefit of an inexact Newton algorithm. We demonstrate that a loosely coupled algorithm is effective and has some advantages, such as reduced storage requirements and smoother transient oscillations. A transonic single-element case converges to 1 ! 10"12 in 90 s on recent commodity hardware, whereas the lift coefficient is converged to three figures in one quarter of that time.