A GMRES fluctuation splitting method for turbomachinery flows

This paper provides an accurate, robust and efficient methodology for solving two-dimentional steady transonic turbomachinery flows. The Euler fluxes are discretized in space using a hybrid multidimentional upwind method, which, according to the local flow conditions, uses the most suitable Fluctuation Splitting (FS) scheme at each cell of the computational domains. 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 by using a preconditioned GMRES strategy. The proposed methodology is employed to compute transonic turbulent flows inside a high-turning turbine-rotor cascade.