RKDG method for 2D gas dynamics simulation on uniform rectangular meshes

Abstract

This paper is devoted to a numerical simulation of 2D gas dynamics flows on uniform rectangular meshes using the Runge - Kutta - Discontinuous - Galerkin (RKDG) method. The RKDG algorithm was implemented with in-house C++ code based on the experience in the investigation of 1D case. The advantage of the RKDG method over the most popular finite volume method (FVM) is discussed: three basis functions being applied in the framework of the RKDG approach lead to a considerable decrease of the numerical dissipation rate with respect to FVM. The results of the acoustic pulse simulation on a sufficiently coarse mesh with the piecewise-linear approximation show a good agreement with the analytical solution in contrast to the FVM numerical solution. For the Sod problem, the results of the discontinuities propagation illustrate the dependence of the scheme resolution on the numerical fluxes, troubled cell indicator and the limitation technique choice. The possibility to resolve strong shocks is demonstrated with the Sedov cylindrical explosion test.