NEW 2-GRID ACCELERATION METHOD FOR UNSTEADY NAVIER-STOKES CALCULATIONS

A quasi-three-dimensional time-marching Navier-Stokes method for calculating unsteady viscous flows in turbomachines is presented. A major feature of the present work is that the time-step limitation in the Navier-Stokes solutions suffered by all explicit time-marching methods is effectively relaxed by using a time-consistent two-grid method. The spatial accuracy is subject to the basic fine mesh, while the coarse mesh, on which the temporal accuracy is guaranteed, is locally applied to the near wall and wake regions to increase the allowable time-step length. The loss of the time accuracy on the basic fine mesh can be easily controlled by choosing a suitable grid size of the coarse mesh according to the wavelength of physical unsteadiness to be dealt with. This two-grid method has been compared with the implicit residual-averaging method and the direct time-marching method for a transonic oscillating cascade flow. Numerical examples for a low-speed oscillating airfoil flow at a dynamic stall condition and a transonic airfoil flow with a self-excited shock oscillation are also presented, in which an increase in the time-step length by a factor of 20 has been achieved.