Total Energy Conservation in ALE schemes for compressible flows

Alain Dervieux (1) , Charbel Farhat (2, 3, 4) , Bruno Koobus (5) , Mariano Vázquez (6)

1 TROPICS - Program transformations for scientific computing
2 ICME - Institute for Computational and Mathematical Engineering [Stanford]
3 Department of Mechanical Engineering [Stanford]
4 AA Stanford - Department of Aeronautics and Astronautics [Stanford]
5 I3M - Institut de Mathématiques et de Modélisation de Montpellier
6 BSC-CNS - Barcelona Supercomputing Center - Centro Nacional de Supercomputacion

The numerical prediction of interaction phenomena between a compressible flow model with a moving domain and other physical models requires that the work performed on the fluid is properly translated into total fluid energy variation. We present a numerical model relying on an Arbitrary Lagrangian-Eulerian (ALE) unstructured vertex-centered finite volume that satisfies this condition together with the Geometric Conservation Law. We apply this numerical scheme to the solution of a 3D fluid-structure interaction problem. The results are contrasted with those obtained by the energy non-conservative counterpart.

Mots clés: Arbitrary Lagrangian Eulerian; compressible flow; spatial discretization; discrete geometric conservation law; total energy conservation

Domaines: Analyse numérique [math.NA]

Alain Dervieux, Charbel Farhat, Bruno Koobus, Mariano Vázquez. Total Energy Conservation in ALE schemes for compressible flows. Revue Européenne de Mécanique Numérique/European Journal of Computational Mechanics, 2010, 19 (4), pp.337-363. ⟨10.3166/ejcm.19.337-363⟩. ⟨hal-00799288⟩