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Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics. (English) Zbl 1156.76039
Summary: This work presents a multi-dimensional cell-centered unstructured finite volume scheme for the solution of multimaterial compressible fluid flows written in Lagrangian formalism. This formulation is considered in the arbitrary Lagrangian-Eulerian framework with the constraint that the mesh velocity and the fluid velocity coincide. The link between the vertex velocity and the fluid motion is obtained by a formulation of the momentum conservation in a class of multi-scale encased volumes around mesh vertices. The vertex velocity is derived with a nodal Riemann solver constructed in such a way that the mesh motion and the face fluxes are compatible. Finally, the resulting scheme conserves both momentum and total energy, and it satisfies a semi-discrete entropy inequality. The numerical results obtained for some classical 2D and 3D hydrodynamic test cases show the robustness and accuracy of the proposed algorithm.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
Software:
CAVEAT
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