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A time semi-implicit scheme for the energy-balanced coupling of a shocked fluid flow with a deformable structure. (English) Zbl 1352.76075

Summary: The objective of this work is to present a conservative coupling method between an inviscid compressible fluid and a deformable structure undergoing large displacements. The coupling method combines a cut-cell Finite Volume method, which is exactly conservative in the fluid, and a symplectic Discrete Element method for the deformable structure. A time semi-implicit approach is used for the computation of momentum and energy transfer between fluid and solid, the transfer being exactly balanced. The coupling method is exactly mass-conservative (up to round-off errors in the geometry of cut-cells) and exhibits numerically a long-time energy-preservation for the coupled system. The coupling method also exhibits consistency properties, such as conservation of uniform movement of both fluid and solid, absence of numerical roughness on a straight boundary, and preservation of a constant fluid state around a wall having tangential deformation velocity. The performance of the method is assessed on test cases involving shocked fluid flows interacting with two and three-dimensional deformable solids undergoing large displacements.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S10 Finite volume methods applied to problems in solid mechanics
76Nxx Compressible fluids and gas dynamics

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References:

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