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Cell-centered discontinuous Galerkin discretization for two-dimensional Lagrangian hydrodynamics. (English) Zbl 1365.76129
Summary: We present a cell-centered discontinuous Galerkin discretization for the two-dimensional gas dynamics equations written using the Lagrangian coordinates related to the initial configuration of the flow, on general unstructured grids. A finite element discretization of the deformation gradient tensor is performed ensuring the satisfaction of the Piola compatibility condition at the discrete level. A specific treatment of the geometry is done, using finite element functions to discretize the deformation gradient tensor. The Piola compatibility condition and the Geometric Conservation law are satisfied by construction of the scheme. The DG scheme is constructed by means of a cellwise polynomial basis of Taylor type. Numerical fluxes at cell interface are designed to enforce a local entropy inequality.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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