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Viscous Stabilizations for High Order Approximations of Saint-Venant and Boussinesq Flows

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Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 119))

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Abstract

Two viscous stabilization methods, namely the spectral vanishing viscosity (SVV) technique and the entropy viscosity method (EVM), are applied to flows of interest in geophysics. First, following a study restricted to one space dimension, the spectral element approximation of the shallow water equations is stabilized using the EVM. Our recent advances are here carefully described. Second, the SVV technique is used for the large-eddy simulation of the spatial and temporal development of the turbulent wake of a sphere in a stratified fluid. We conclude with a parallel between these two stabilization techniques.

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Acknowledgements

Part of this work was made at the Dpt of Mathematics of National Taiwan University in the frame of the Inria project AMOSS.

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Authors and Affiliations

  1. Université Côte d’Azur, CNRS, Inria, LJAD, Nice, France

    Richard Pasquetti

  2. Lab. J.A. Dieudonné (CASTOR project), Parc Valrose, 06108, Nice Cedex 2, France

    Richard Pasquetti

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  1. Richard Pasquetti
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Correspondence to Richard Pasquetti .

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Editors and Affiliations

  1. School of Mechanical Engineering, University of Campinas, Campinas, Brazil

    Marco L. Bittencourt

  2. Department of Civil Engineering, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil

    Ney A. Dumont

  3. EPFL-SB-MATHICSE-MCSS, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Jan S. Hesthaven

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Pasquetti, R. (2017). Viscous Stabilizations for High Order Approximations of Saint-Venant and Boussinesq Flows. In: Bittencourt, M., Dumont, N., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016. Lecture Notes in Computational Science and Engineering, vol 119. Springer, Cham. https://doi.org/10.1007/978-3-319-65870-4_37

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