Abstract
The numerical method based on the discontinuous Galerkin (DG) approach for perfect inviscid compressible gas dynamics modelling is developed. The approximate Riemann solvers in combination with gas dynamics equations system characteristic properties are used to calculate the numerical fluxes on the cells interfaces and inside the cells. A number of approximate Riemann solvers are considered. The solution characteristic decomposition is used in the similar to PPML way. The developed algorithm is tested using problems with smooth and discontinuous solutions. Both one-dimensional and two-dimensional test problems are considered. The method provides accurate discontinuity resolution and ability to compute gas-dynamic instabilities with minimal artificial distortion.
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