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Local Preconditioning Techniques Coupled with a Variational Multiscale Method to Solve Compressible Steady Flows at Low Mach Numbers

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Computational Science and Its Applications – ICCSA 2019 (ICCSA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11621))

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Abstract

In this work we evaluate a combination of the Weiss-Smith and Choi-Merkle local preconditioners coupled with the density-based Nonlinear Multiscale Viscosity (NMV) finite element method for solving steady compressible flows at low Mach numbers. The multiscale formulation is based on the strategy of separating scales, in which the subgrid scale space is spanned by bubble functions, allowing to use a static condensation procedure in the local matrix system to define the resolved scale problem. Also, a residual-based nonlinear viscosity operator is added to the Galerkin formulation in order to obtain a stabilized formulation. As density-based methods do not work well in problems with Mach numbers tending to zero, resulting in a degradation of the solution accuracy, the resulting numerical method gathering those two approaches allows to solve compressible flows in the incompressible limit. We evaluate this methodology simulating a steady flow over the NACA 0012 airfoil under some regimes of inflow Mach numbers. The numerical result exhibits promising solutions to compressible flow problems in the incompressible limit.

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References

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Acknowledgments

The authors would like to thank the support through the Espírito Santo State Research Support Foundations (FAPES).

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Authors and Affiliations

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

    Sérgio Souza Bento & Isaac P. Santos

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

    Isaac P. Santos & Lucia Catabriga

  3. Department of Mechanical Engineering, Federal Institute of Espírito Santo, Aracruz, ES, Brazil

    Leonardo Muniz de Lima

Authors
  1. Sérgio Souza Bento
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  2. Leonardo Muniz de Lima
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  3. Isaac P. Santos
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  4. Lucia Catabriga
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Corresponding author

Correspondence to Sérgio Souza Bento .

Editor information

Editors and Affiliations

  1. Covenant University, Ota, Nigeria

    Sanjay Misra

  2. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  3. University of Basilicata, Potenza, Italy

    Beniamino Murgante

  4. Saint Petersburg State University, Saint Petersburg, Russia

    Elena Stankova

  5. Saint Petersburg State University, Saint Petersburg, Russia

    Vladimir Korkhov

  6. Polytechnic University of Bari, Bari, Italy

    Carmelo Torre

  7. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  8. Monash University, Clayton, VIC, Australia

    David Taniar

  9. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  10. Polytechnic University of Bari, Bari, Italy

    Eufemia Tarantino

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Bento, S.S., de Lima, L.M., Santos, I.P., Catabriga, L. (2019). Local Preconditioning Techniques Coupled with a Variational Multiscale Method to Solve Compressible Steady Flows at Low Mach Numbers. In: Misra, S., et al. Computational Science and Its Applications – ICCSA 2019. ICCSA 2019. Lecture Notes in Computer Science(), vol 11621. Springer, Cham. https://doi.org/10.1007/978-3-030-24302-9_12

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  • DOI: https://doi.org/10.1007/978-3-030-24302-9_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-24301-2

  • Online ISBN: 978-3-030-24302-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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