Higher Order KFVS Algorithms Using Compact Upwind Difference Operators

A family of high order accurate compact upwind difference operators have been used, together with the split fluxes of the KFVS (kinetic flux vector splitting) scheme to obtain high order semidiscretizations of the 2D Euler equations of inviscid gas dynamics in general coordinates. A TVD multistage Runge?Kutta time stepping scheme is used to compute steady states for selected transonic/supersonic flow problems which indicate the higher accuracy and low diffusion realizable in such schemes.