Complete Flux Scheme for Compressible Flow Computation

In the complete flux scheme, the numerical flux at a cell interface is computed from the complete differential equation, including the source term. This way we get a numerical flux consisting of two parts, i.e.,the homogeneous flux, corresponding to the advection-diffusion operator and the inhomogeneous flux corresponding to the source term. The numerical flux behaves second order accurate, uniformly in the local Peclet numbers. We have combined the complete flux scheme with the cell-centred finite volume method and the resulting numerical scheme is second order accurate and is not prone to spurious oscillations, even for dominant advection. In this book we derive one-dimensional steady flow model from the Navier-Stokes equations. We present the analysis of this model and the behavior of the numerical solution using the complete flux scheme.