A GMRES fluctuation splitting method for steady viscous flows.

This paper provides an accurate, robust, and efficient methodology for solving steady transonic turbomachinery flows. The Euler fluxes are discretized in space using a hybrid multidimensional upwind method, which, according to the local flow conditions, uses the most suitable Fluctuation Splitting (FS) scheme at each cell of the computational domain. The viscous terms are discretized using a standard Galerkin finite element scheme. The eddy viscosity is evaluated by means of the Spalart-Allmaras turbulence transport equation, which is discretized in space by means of a mixed FS-Galerkin approach. The equations are discretized in time using an implicit Euler scheme, the Jacobians being evaluated by two-point backward differences. The resulting large sparse linear systems are solved sequentially using a preconditioned GM-RES strategy. The proposed methodology is employed to compute the 2D subsonic and transonic turbulent flows inside a high-turning turbine-rotor cascade, as well as a 3D subsonic turbulent flow inside the Stanitz elbow.