In general, it would be extremely difficult to generate a single grid that would adequately discretize the complex and unsteady, rotating geometries found within a turbomachine. A zonal method is used by the STAGE codes to provide a good discretization of the geometry while allowing for movement between rotor and stator airfoils. A typical two-dimensional zonal grid system for a single passage through the midspan region of a compressor is shown in Figure 1. In this orientation, the flow enters the compressor from the left, progresses through the inlet guide vane (IGV) and the two rotor-stator pairs and exits the system to the right. The flow field around each airfoil is discretized using two grids. Inner "O" grids are clustered near the airfoil surfaces to support viscous gradients generated by the surfaces. The inner grids are overlaid on outer "H" grids which support the largely inviscid flow field in the passages between the airfoils. Bilinear interpolation is used to transfer data between grids. For the two-dimensional algorithm, the thin-layer Navier-Stokes equations are applied in the inner grids and the Euler equations are used in the outer grids. For three-dimensional simulations, these annular two-dimensional grids are stacked in the radial direction to form a fully three-dimensional zonal grid system. In three dimensions, the inner and outer grid surfaces coincide with the hub and tip casings, so the thin-layer Navier-Stokes equations are also solved in the outer "H" grids.
This grid topology requires two grids per airfoil for both two- and three-dimensional calculations. In addition, inlet and exit grids are used to compute the flow in the inflow and outflow regions of the turbomachine. For the five airfoil compressor shown in Figure 1, 12 grids are then required to fully discretize the midspan compressor geometry for both two- and three-dimensional computations.