The numerical approach uses a hybrid structured-unstructured zonal grid topology along with modeling equations and solution techniques that are most appropriate in the individual domains, thus combining the advantages of both structured and unstructured grid methods. The viscous flow region in the immediate vicinity of the airfoils is resolved using a third-order accurate, implicit, upwind solution of the Navier-Stokes equations on structured, O-type grids. Explicit solutions of the Euler equations are obtained in the rest of the domain that consists of an unstructured mesh made up of triangular cells.
The use of both central- and upwind-differenced flux schemes is investigated for the unstructured domains. Methodologies for accurate, conservative transfer of information at the interface between the structured and unstructured domains as well as that between two unstructured grids in relative motion are developed. An efficient and robust solution adaptation strategy is developed which incorporates both refinement and de-refinement capabilities for the unstructured grid regions.
The figure shows the composite grid used in computing the unsteady flowfield in a single stage axial turbine. The calculation was performed with 3 stator and 4 rotor airfoils. The structured ``O'' grids around the individual airfoils consist of $181\times 20$ points and the unstructured meshes in the outer zones of the stator and rotor rows have 11360 and 13707 points respectively. The grids of the rotor zone move past the stator in time along a sliding interface located midway between the airfoils. The grid in the figure is colored by the instantaneous pressure values at each location.