A Self-adapting LPS Solver for Laminar and Turbulent Fluids in Industry and Hydrodynamic Flows

  • Tomás Chacón Rebollo
  • Enrique Delgado Ávila
  • Macarena Gómez Mármol
  • Samuele Rubino
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)


In this work we address the solution of the Navier–Stokes equations (NSE) in turbulent regime. On one side we focus is on the high-order term-by-term stabilization method that has one level, in the sense that it is defined on a single mesh, and in which the projection-stabilized structure of standard LPS methods is replaced by an interpolation-stabilized structure. The interest of LPS methods is that it ensures a self-adapting high accuracy in laminar regions of a turbulent flow, that turns to be of overall optimal high accuracy if the flow is fully laminar. On another side we present a reduced basis Smargorinsky turbulence model, based upon an empirical interpolation of the eddy viscosity term. This method yields dramatical improvements of the computing time, over 1000, for benchmark flows.



The research of Tomás Chacón Rebollo and Macarena Gómez Mármol has been partially supported by the Spanish Government Project MTM2015-64577-C2-1-R. The research of Samuele Rubino has been partially supported by the Junta de Andalucía Excellence Project P12-FQM-454. Samuele Rubino would also gratefully acknowledge the financial support received from ERC Project H2020-EU.1.1.-639227 during his postdoctoral research involved in this article.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Tomás Chacón Rebollo
    • 1
  • Enrique Delgado Ávila
    • 1
  • Macarena Gómez Mármol
    • 2
  • Samuele Rubino
    • 3
  1. 1.Departamento EDAN & IMUSUniversidad de SevillaSevillaSpain
  2. 2.Departamento EDANUniversidad de SevillaSevillaSpain
  3. 3.Departamento de Análisis Matemático & IMUSUniversidad de SevillaSevillaSpain

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