Positivity statements for a mixed-element-volume scheme on fixed and moving grids

Paul-Henri Cournède Bruno Koobus Alain Dervieux

Article in Revue européenne de mécanique numérique (32 pages)

Abstract: This paper considers a class of second-order accurate vertex-centered mixed finite-element finite-volume MUSCL schemes. These schemes apply to unstructured triangulations and tetrahedrizations and fluxes are computed on an edge basis. We dene conditions under which these schemes satisfy a density-positivity statement for Euler flows, a maximum principle for a scalar conservation law and a multicomponent flow. This extends to an Arbitrary Lagrangian-Eulerian formulation. Steady and unsteady flow simulations illustrate the accuracy and the robustness of these schemes.

Keywords: finite-element, finite-volume, positivity, maximum principle, scalar conservation law, Euler, ALE, multi-component, fluid-structure interaction

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@article{CKD06,
  author = {Courn{\`e}de, P.-H. and Koobus, B. and Dervieux, A.},
  title = {Positivity statements for a mixed-element-volume scheme on fixed and moving grids},
  journal = {Revue europ{\'e}enne de m{\'e}canique num{\'e}rique},
  Volume = 15,
  Number = {7-8},
  pages = "767-799",
  year = 2006