Hybrid central-upwind finite volume schemes for solving the Euler and Navier–Stokes equations

A novel method based on the hybridization of central schemes and upwind schemes is proposed for finite volume discretization of the Euler and Navier–Stokes equations on multi-blocked structured grids. The developed methodology takes the advantages of the low diffusion characteristic from an improved central scheme and the discontinuity-capturing capability from a characteristic-based upwind scheme. A simple and efficient improvement to the scalar dissipation and matrix dissipation model for the central scheme is suggested to enhance the accuracy of the existing methods. The resulting hybrid schemes are as compact as the underlying finite volume methods and therefore easy to implement. Numerical results for a wide range of flow conditions demonstrate the method simultaneously obtains the desired accuracy and sharp, oscillation-free shock transition for both the inviscid and viscous simulation.