A Zonal Approach for Solving the Compressible Navier-Stokes Equations Using a TVD Finite Volume Method

A new zonal approach for compressible viscous flow computations using a TVD finite volume method has been developed. The two-dimensional. Reynolds-averaged NavierStokes equations are discretized spatially by the finite volume formulation. The inviscid fluxes at the cell interfaces are evaluated through the MUSCLtype approach of an upwind scheme. In the present approach, the computational domain is divided into non-overlapping zones. The zonal boundaries are constructed from the cell interfaces, since the finite volume formulation with the cell-centered control volumes is used. Consequently communication from one zone to another is accomplished by the numerical fluxes through the zonal boundaries. The use of the finite volume formulation can ensure the unity of zonal boundaries and the complete conservation of numerical fluxes at the zonal boundaries, which results in a high-accuracy zonal approach. In order to demonstrate the versatility of the present zonal approach, numerical results are presented for viscous flows through a transonic turbine cascade.