Accuracy analysis of central schemes with artificial dissipation and upwind flux‐difference tvd schemes for navier‐stokes equations

Abstract

A comparison of the accuracy of the central discretization scheme with artificial dissipation and the upwind flux‐difference TVD scheme has been made for the compressible Navier‐Stokes equations for high Reynolds number flows. First, a comparison is made on two one‐dimensional model problems. Then the schemes are compared on flat plate boundary layer flow. It is shown that a central scheme basically has poor accuracy due to the isotropic nature of the artificial dissipation. An upwind scheme decomposes the flow into different components and adapts the dissipation to the velocity of the components. The associated ansitropic dissipation results in a good accuracy. It is further discussed how a central discretization scheme with artificial dissipation can be improved at the expense of the same complexity of an upwind scheme.