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On a robust discontinuous Galerkin technique for the solution of compressible flow. (English) Zbl 1114.76042
Summary: We describe a numerical technique allowing the solution of compressible inviscid flow with a wide range of Mach numbers. The method is based on the application of discontinuous Galerkin finite element method for the space discretization of Euler equations written in conservative form, combined with a semi-implicit time discretization. Special attention is paid to the treatment of boundary conditions and to the stabilization of the method in the vicinity of discontinuities avoiding Gibbs phenomenon. As a result, we obtain a technique allowing the numerical solution of flows with practically all Mach numbers without any modification of Euler equations. This means that the proposed method can be used for solution of high-speed flows as well as low Mach number flows. Presented numerical tests prove the accuracy of the method and its robustness with respect to Mach number.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
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