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

Abstract

A new zonal approach for compressible viscous flow computation using a TVD finite volume method has been developed. The two-dimensional, Reynolds-averaged Navier-Stokes equations are discretized spatially by a cell-centered finite volume formulation. The inviscid fluxes at cell interfaces are evaluated through the MUSCL-type approach of an upwind scheme. The viscous fluxes are determined in a central differencing manner. In the present approach, the computational domain is divided into nonoverlapping 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 numerical fluxes through the zonal boundaries. The use of the finite volume formulation can ensure the uniqueness of the zonal boundaries and the complete conservation of the numerical fluxes across the zonal boundaries, which results in a highly accurate 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.