Numerical modelling of two-dimensional perfect gas flows using RKDG method on unstructured meshes

This paper is devoted to the simulation of the two-dimensional gas flows with oscillations and discontinuities using the Runge — Kutta Discontinuous Galerkin (RKDG) method, that has been implemented in the code prototype written in C++. It implements the HLLC numerical flux, the KXRCF troubled cells indicator, the WENO S limiter with the local characteristic decomposition approach and algorithm of dynamic time step control. The computations could be performed on unstructured meshes with mixed cell types (quadrangular and triangular) which can be built in any mesh bulder in IDEAS UNV format (i.e. SALOME). The code is verified on the common numerical tests such as pulsating and vibrating cylinders, Sod-like cylindrical explosion, forward-facing step, blast wave problem. Comparison between analytical solution and numerical results obtained with the in-house code and the open-source OpenFOAM package is presented.