A Two-Dimensional Central Non-Oscillatory Scheme for Inviscid Compressible Flows

Abstract

For this study, we developed a two-dimensional high order finite volume method code to solve inviscid compressible flows. In particular, the central essentially non-oscillatory (CENO) scheme improves spatial reconstruction, and the Runge-Kutta 4 th order scheme enhances temporal accuracy. The CENO scheme provides a smoothness indicator that dictates whether a cell is under-resolved. One can evaluate this indicator either with the first or second layer of each cell's neighbours, where it is applicable. For under-resolved cells, the reconstruction switches to limited second order instead of high order. We solved the shock tube in terms of accuracy and computational time for different spatial high order reconstructions. Results showed that for problems which present discontinuities, the usage of high order schemes to enhance spatial reconstruction does not improve accuracy as expected. Furthermore, the presence of discontinuities effects also the order of convergence of the solver. Specifically the order of convergence for all the studied spatial reconstructions is always as first order.