A new zonal approach for computation of compressible viscous flows in cascades has been developed. The two-dimensional, Reynolds-averaged Navier–Stokes equations are discretized spatially by a cell-centered finite volume formulation. In order to make the present approach robust, the inviscid fluxes at cell interfaces are evaluated using a highly accurate TVD scheme based on the MUSCL-type approach with the Roe’s approximate Riemann solver. The viscous fluxes are determined in a central differencing manner. To simplify the grid generation, a composite zonal grid system is adopted, in which the computational domain is divided into nonoverlapping zones, and structured grids are generated independently in each zone. The zonal boundary between two zones is uniquely defined by cell interfaces of one zone, which ensures the uniqueness of the zonal boundary. Communication from one zone to the other is accomplished by numerical fluxes across the zonal boundary. It should be noted that the complete conservation of the numerical fluxes across the zonal boundary can be satisfied by directly evaluating the numerical fluxes using the finite volume method and by ensuring the uniqueness of the zonal boundary. In order to demonstrate the versatility of the present zonal approach, numerical examples are presented for viscous flows through a transonic turbine cascade.

Furukawa, M., Yamasaki, M., & Inoue, M. (1991). A Zonal Approach for Navier–Stokes Computations of Compressible Cascade Flow Fields Using a TVD Finite Volume Method. Journal of Turbomachinery, 113(4), 573–582.