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

  • V. Korchagova
  • I. Fufaev
  • V. Lukin
  • I. Marchevsky
  • S. Sautkina
Abstract.

This paper is devoted to a numerical simulation of 2D gas dynamics flows onuniform rectangular meshes using the Runge – Kutta – Discontinuous – Galerkin (RKDG)method. The RKDG algorithm was implemented with in-house C++ code based on theexperience in the investigation of 1D case. The advantage of the RKDG method over the mostpopular finite volume method (FVM) is discussed: three basis functions being applied in theframework of the RKDG approach lead to a considerable decrease of the numerical dissipationrate with respect to FVM. The results of the acoustic pulse simulation on a sufficiently coarsemesh with the piecewise-linear approximation show a good agreement with the analyticalsolution in contrast to the FVM numerical solution. For the Sod problem, the results of thediscontinuities propagation illustrate the dependence of the scheme resolution on the numericalfluxes, troubled cell indicator and the limitation technique choice. The possibility to resolvestrong shocks is demonstrated with the Sedov cylindrical explosion test.

Edition: Irreversible Processes in Nature and Technics. Journal of Physics: Conference Series. 1348 (2019) 012098.
DOI: 10.1088/1742-6596/1348/1/012098