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Finite Volume Formulation of a Third-Order Residual-Based Compact Scheme for Unsteady Flow Computations

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High Order Nonlinear Numerical Schemes for Evolutionary PDEs

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 99))

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Abstract

The paper discusses the design principles of a Finite-Volume Residual-Based Compact (RBC) scheme for the spatial discretization of the unsteady compressible governing equations of gas dynamics on general structured meshes. The scheme makes use of weighted approximations that allow to ensure high accuracy while taking benefit from the structured nature of the grid. The stability properties of the proposed spatial approximation are discussed. Numerical applications to unsteady compressible flows demonstrate the advantages of the proposed formulation with respect to straightforward extensions of RBC schemes.

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Acknowledgements

This research has been done within the framework of the European project IDIHOM (Industrialization of High Order Methods) which aims to promote the use of high-order numerical methods by the European aerospace industry.

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Authors and Affiliations

  1. DynFluid Laboratory, Arts et Métiers-ParisTech, 151 bd. de l’Hopital, 75013, Paris, France

    Karim Grimich, Paola Cinnella & Alain Lerat

  2. Département de Simulation Numérique des Ecoulements et Aéroacoustique, ONERA, 29 Avenue de la Division Leclerc, FR-92322, Chatillon Cedex, France

    Bertrand Michel

Authors
  1. Karim Grimich
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  2. Bertrand Michel
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  3. Paola Cinnella
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  4. Alain Lerat
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Corresponding author

Correspondence to Paola Cinnella .

Editor information

Editors and Affiliations

  1. Institute of Mathematics, University of Zurich, Zurich, Switzerland

    Rémi Abgrall

  2. INRIA and Institut Polytechnique de Bordeaux, Institut de Mathématiques de Bordeaux, Talence, France

    Héloïse Beaugendre

  3. INRIA, Institut de Mathématiques de Bordeaux, Talence, France

    Pietro Marco Congedo

  4. INRIA and Institut Polytechnique de Bordeaux, Institut de Mathématiques de Bordeaux, Talence, France

    Cécile Dobrzynski

  5. INRIA, Laboratoire de Mathématiques et de leurs Applications, Pau, France

    Vincent Perrier

  6. INRIA, Institut de Mathématiques de Bordeaux, Talence, France

    Mario Ricchiuto

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Grimich, K., Michel, B., Cinnella, P., Lerat, A. (2014). Finite Volume Formulation of a Third-Order Residual-Based Compact Scheme for Unsteady Flow Computations. In: Abgrall, R., Beaugendre, H., Congedo, P., Dobrzynski, C., Perrier, V., Ricchiuto, M. (eds) High Order Nonlinear Numerical Schemes for Evolutionary PDEs. Lecture Notes in Computational Science and Engineering, vol 99. Springer, Cham. https://doi.org/10.1007/978-3-319-05455-1_3

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