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A cell-centered Lagrangian scheme for two-dimensional compressible flow problems

P.H. Maire 1 Remi Abgrall 2, 3 Jérôme Breil 1 Jean Ovadia 4
3 SCALAPPLIX - Algorithms and high performance computing for grand challenge applications
INRIA Futurs, Université Bordeaux Segalen - Bordeaux 2, Université Sciences et Technologies - Bordeaux 1, École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), CNRS - Centre National de la Recherche Scientifique : UMR5800
Abstract : We present a new Lagrangian cell-centered scheme for two-dimensional compressible flows. The primary variables in this new scheme are cell-centered, i.e., density, momentum, and total energy are defined by their mean values in the cells. The vertex velocities and the numerical fluxes through the cell interfaces are not computed independently, contrary to standard approaches, but are evaluated in a consistent manner due to an original solver located at the nodes. The main new feature of the algorithm is the introduction of four pressures on each edge, two for each node on each side of the edge. This extra degree of freedom allows us to construct a nodal solver which fulfills two properties. First, the conservation of momentum and total energy is ensured. Second, a semidiscrete entropy inequality is provided. In the case of a one-dimensional flow, the solver reduces to the classical Godunov acoustic solver: it can be considered as its two-dimensional generalization. Many numerical tests are presented. They are representative test cases for compressible flows and demonstrate the robustness and the accuracy of this new solver.
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Contributor : Rémi Abgrall <>
Submitted on : Friday, October 24, 2008 - 2:43:39 PM
Last modification on : Thursday, February 11, 2021 - 2:46:02 PM


  • HAL Id : inria-00334022, version 1



P.H. Maire, Remi Abgrall, Jérôme Breil, Jean Ovadia. A cell-centered Lagrangian scheme for two-dimensional compressible flow problems. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2007, 29 (4), pp.1781-1824. ⟨inria-00334022⟩



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