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A Multiscale Finite Element Formulation for the Incompressible Navier-Stokes Equations

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Computational Science and Its Applications – ICCSA 2018 (ICCSA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10961))

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Abstract

In this work we present a variational multiscale finite element method for solving the incompressible Navier-Stokes equations. The method is based on a two-level decomposition of the approximation space and consists of adding a residual-based nonlinear operator to the enriched Galerkin formulation, following a similar strategy of the method presented in [1, 2] for scalar advection-diffusion equation. The artificial viscosity acts adaptively only onto the unresolved mesh scales of the discretization. In order to reduce the computational cost typical of two-scale methods, the subgrid scale space is defined using bubble functions whose degrees of freedom are locally eliminated in favor of the degrees of freedom that live on the resolved scales. Accuracy comparisons with the streamline-upwind/Petrov-Galerkin (SUPG) formulation combined with the pressure stabilizing/Petrov-Galerkin (PSPG) method are conducted based on 2D benchmark problems.

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Authors and Affiliations

  1. High Performance Computing Lab, Federal University of Espírito Santo, Vitória, ES, Brazil

    Riedson Baptista, Sérgio S. Bento, Isaac P. Santos, Leonardo M. Lima, Andrea M. P. Valli & Lucia Catabriga

  2. Department of Applied Mathematics, Federal University of Espírito Santo, São Mateus, ES, Brazil

    Riedson Baptista, Sérgio S. Bento & Isaac P. Santos

Authors
  1. Riedson Baptista
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  2. Sérgio S. Bento
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  3. Isaac P. Santos
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  4. Leonardo M. Lima
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  5. Andrea M. P. Valli
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  6. Lucia Catabriga
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Corresponding author

Correspondence to Riedson Baptista .

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Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Italy

    Beniamino Murgante

  3. Covenant University, Ota, Nigeria

    Sanjay Misra

  4. Saint Petersburg State University, Saint Petersburg, Russia

    Elena Stankova

  5. Polytechnic University of Bari, Bari, Italy

    Carmelo M. Torre

  6. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  7. Monash University, Clayton, Victoria, Australia

    David Taniar

  8. Kyushu Sangyo University, Fukuoka shi, Fukuoka, Japan

    Bernady O. Apduhan

  9. Politecnico di Bari, Bari, Italy

    Eufemia Tarantino

  10. Myongji University, Yongin, Korea (Republic of)

    Yeonseung Ryu

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Baptista, R., Bento, S.S., Santos, I.P., Lima, L.M., Valli, A.M.P., Catabriga, L. (2018). A Multiscale Finite Element Formulation for the Incompressible Navier-Stokes Equations. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2018. ICCSA 2018. Lecture Notes in Computer Science(), vol 10961. Springer, Cham. https://doi.org/10.1007/978-3-319-95165-2_18

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  • DOI: https://doi.org/10.1007/978-3-319-95165-2_18

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