Implicit Time-Steppign Methods for the navier-Stokes Equations

摘要

Time-stepping methods to simulate turbulent, compressible and transonic flows about aerofoils and wings are presnted. For aerofoils, the method consists of a preconditioned conjugate gradient solution of the linear system obtained at each implicit time step. The preconditioning strategy is based ont he standard ADI factorisation. Results are presented for steady transonic flow, the flow around a pitching aerofoil and the nonlienar aeroelastic response of an aerofoil. The equations of motion and the coupling with the flow solver for the aeroelastic case are discussed. A novel time stepping method for three-dimensional flows is presented. This method uses a two factor approximate factorisation of the linear system at each implicit step. The complicated factors arising from streamwise slices are solved by the method presented for aerofoil flows. This approach yields more favourable stability properties than the usual three factor method and has low memory requirements. Results are shown for a steady flow over the ONERA M6 wing.