Evaluation of TVD high resolution schemes for unsteady viscous shocked flows

Abstract

The goal of this study is to evaluate the accuracy of several high resolution total variation diminishing schemes in solving complex unsteady viscous shocked flows. Two types of discretization, namely a combined time and space discretization, and an independent time and space discretization are considered. Both methods are associated with several limiters, among which a more accurate new family of limiters depending on the local wave velocity. The accuracy properties of each scheme are first reviewed on inviscid 1D and 2D test cases, in order to establish a ranking with respect to their dissipative error. We then study the flow produced by the interaction of a reflected shock wave with the incident boundary layer in a shock tube. The calculations are performed for two values of the Reynolds number. At Re=200, convergence is attained and it is shown that the combined time and space discretization method converges faster. Good classical limiters do almost the same job as the new family of limiters. When the Reynolds number is increased to the value of 1000, the flow becomes much more complex. Although convergence is hard to reach, the close examination of the results leads us to conclude that the combined time and space discretization method associated with the new limiter gives from far the best results.