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Finite Element Approximation of an Unsteady Projection-Based VMS Turbulence Model with Wall Laws

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Boundary and Interior Layers, Computational and Asymptotic Methods - BAIL 2014

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 108))

Abstract

In this work we present the numerical analysis and study the performance of a finite element projection-based Variational MultiScale (VMS) turbulence model that includes general non-linear wall laws. We introduce Lagrange finite element spaces adapted to approximate the slip condition. The sub-grid effects are modeled by an eddy diffusion term that acts only on a range of small resolved scales. Moreover, high-order stabilization terms are considered, with the double aim to guarantee stability for coarse meshes, and help to counter-balance the accumulation of sub-grid energy together with the sub-grid eddy viscosity term. We prove stability and convergence for solutions that only need to bear the natural minimal regularity, in unsteady regime. We also study the asymptotic energy balance of the system. We finally include some numerical tests to assess the performance of the model described in this work.

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Acknowledgements

Research partially supported by the Spanish Government project MTM2012-36124-C02-01.

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Authors and Affiliations

  1. Dpto. de Ecuaciones Diferenciales y Análisis Numérico & IMUS, Universidad de Sevilla, Seville, Spain

    Tomás Chacón Rebollo & Samuele Rubino

  2. Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Seville, Spain

    Macarena Gómez Mármol

Authors
  1. Tomás Chacón Rebollo
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  2. Macarena Gómez Mármol
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  3. Samuele Rubino
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Corresponding author

Correspondence to Tomás Chacón Rebollo .

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Editors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University in Prague, Praha, Czech Republic

    Petr Knobloch

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Rebollo, T.C., Mármol, M.G., Rubino, S. (2015). Finite Element Approximation of an Unsteady Projection-Based VMS Turbulence Model with Wall Laws. In: Knobloch, P. (eds) Boundary and Interior Layers, Computational and Asymptotic Methods - BAIL 2014. Lecture Notes in Computational Science and Engineering, vol 108. Springer, Cham. https://doi.org/10.1007/978-3-319-25727-3_5

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