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Discontinuous Galerkin solution of compressible flow in time-dependent domains. (English) Zbl 1425.76212
Summary: This work is concerned with the simulation of inviscid compressible flow in time-dependent domains. We present an arbitrary Lagrangian-Eulerian (ALE) formulation of the Euler equations describing compressible flow, discretize them in space by the discontinuous Galerkin method and introduce a semi-implicit linearized time stepping for the numerical solution of the complete problem. Special attention is paid to the treatment of boundary conditions and the limiting procedure avoiding the Gibbs phenomenon in the vicinity of discontinuities. The presented computational results show the applicability of the developed method.

76N15 Gas dynamics (general theory)
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
Full Text: DOI
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