Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics

  • Authors:

  • Pierre-Henri Maire;Boniface Nkonga

  • Affiliations:

  • UMR CELIA, Université Bordeaux I, 351 Cours de la Libération, 33 405 Talence, France;IMB, INRIA Bordeaux-Sud Ouest, Université Bordeaux I, 351 Cours de la Libération, 33 405 Talence, France

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

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Abstract

This work presents a multi-dimensional cell-centered unstructured finite volume scheme for the solution of multimaterial compressible fluid flows written in the Lagrangian formalism. This formulation is considered in the Arbitrary-Lagrangian-Eulerian (ALE) 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 on 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 the accuracy of the proposed algorithm.