Third-order numerical scheme for Euler equations of gas dynamics using Jordan canonical based splitting flux

Abstract

We propose third-order A-WENO finite difference schemes that are based on the recently introduced first-order numerical schemes in [N. K. Garg et al., Journal of Computational Physics, 407(2020)] for the systems of compressible Euler equations of gas dynamics. The convective components of these schemes (fluxes), both in one- and multi-dimensions, are free from complicated Riemann solvers. Third-order characteristic-wise WENO-Z interpolations are employed to obtain the third-order point values required for the numerical fluxes. To demonstrate the robustness and accuracy of the resulting schemes, we compare the numerical results with local Lax–Friedrichs (LLF) and Harten–Lax–van Leer (HLL) fluxes on various one- and two-dimensional examples. The obtained results outperform LLF and HLL fluxes in terms of enhancing the resolution of contact waves, especially near isolated steady and moving contact discontinuities, as well as in accurately resolving high-frequency waves in one dimension (1-D) and the small-scale structures in two dimensions (2-D).