Evaluation of some high-order shock capturing schemes for direct numerical simulation of unsteady two-dimensional free flows

Abstract

The present study addresses the capability of a large set of shock-capturing schemes to recover the basic interactions between acoustic, vorticity and entropy in a direct numerical simulation (DNS) framework. The basic dispersive and dissipative errors are first evaluated by considering the advection of a Taylor vortex in a uniform flow. Two transonic cases are also considered. The first one consists of the interaction between a temperature spot and a weak shock. This test emphasizes the capability of the schemes to recover the production of vorticity through the baroclinic process. The second one consists of the interaction of a Taylor vortex with a weak shock, corresponding to the framework of the linear theory of Ribner. The main process in play here is the production of an acoustic wave. The results obtained by using essentially non-oscillatory (ENO), total variation diminishing (TVD), compact-TVD and MUSCL schemes are compared with those obtained by means of a sixth-order accurate Hermitian scheme, considered as reference. The results are as follows; the ENO schemes agree pretty well with the reference scheme. The second-order accurate Upwind-TVD scheme exhibits a strong numerical diffusion, while the MUSCL scheme behavior is very sensitive to the value on the parameter β in the limiter function minmod. The compact-TVD schemes do not yield improvement over the standard TVD schemes. Copyright © 2000 John Wiley & Sons, Ltd.