A cubic-spline-based time collocation method applied to simulate periodic transonic flows

A cubic-spline-based time collocation method is used to solve periodic transonic flows for aeroelastic analysis. The time periodical flow variables are first approximated by cubic splines, and then the time-derivative terms are represented by a source term, which couples the flow solutions at all the sampled time instants. Simulation of two transonic external unsteady flows, including the oscillating NACA 0012 aerofoil and pitching rectangular supercritical wing, were carried out. The cubic-spline-based time collocation method with relatively small number of time instants sampled demonstrate high accuracy, whilst it is several times faster than the conventional time-marching method. The effect of different basis function used in the time collocation methods are also studied by comparing the results to that of the state-of-the-art time spectral method. This method was also validated against aeroelastic experimental data of the vibrating STCF 11 turbine blades. Only single passage computational mesh is involved by adopting the phase-lag periodic conditions. Good accuracy of the proposed time collocation method is also achieved and about one order of speed-up is obtained as compared with time-marching simulation.