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A second-order cell-centered Lagrangian ADER-MOOD finite volume scheme on multidimensional unstructured meshes for hydrodynamics. (English) Zbl 1381.76212
Summary: In this paper, we develop a conservative cell-centered Lagrangian finite volume scheme for the solution of the hydrodynamics equations on unstructured multidimensional grids. The method is derived from the Eucclhyd scheme discussed in [P.-H. Maire et al., SIAM J. Sci. Comput. 29, No. 4, 1781–1824 (2007; Zbl 1251.76028); Int. J. Numer. Methods Fluids 65, No. 11–12, 1281–1294 (2011; Zbl 1429.76089); Comput. Fluids 46, No. 1, 341–347 (2011; Zbl 1433.76137)]. It is second-order accurate in space and is combined with the a posteriori multidimensional optimal order detection (MOOD) limiting strategy to ensure robustness and stability at shock waves. Second-order of accuracy in time is achieved via the ADER (Arbitrary high order schemes using DERivatives) approach. A large set of numerical test cases is proposed to assess the ability of the method to achieve effective second order of accuracy on smooth flows, maintaining an essentially non-oscillatory behavior on discontinuous profiles, general robustness ensuring physical admissibility of the numerical solution, and precision where appropriate.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
76L05 Shock waves and blast waves in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
Software:
HE-E1GODF; MOOD
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