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Stabilization and discontinuity-capturing parameters for space–time flow computations with finite element and isogeometric discretizations

  • Kenji Takizawa
  • Tayfun E. Tezduyar
  • Yuto Otoguro
Original Paper

Abstract

Stabilized methods, which have been very common in flow computations for many years, typically involve stabilization parameters, and discontinuity-capturing (DC) parameters if the method is supplemented with a DC term. Various well-performing stabilization and DC parameters have been introduced for stabilized space–time (ST) computational methods in the context of the advection–diffusion equation and the Navier–Stokes equations of incompressible and compressible flows. These parameters were all originally intended for finite element discretization but quite often used also for isogeometric discretization. The stabilization and DC parameters we present here for ST computations are in the context of the advection–diffusion equation and the Navier–Stokes equations of incompressible flows, target isogeometric discretization, and are also applicable to finite element discretization. The parameters are based on a direction-dependent element length expression. The expression is outcome of an easy to understand derivation. The key components of the derivation are mapping the direction vector from the physical ST element to the parent ST element, accounting for the discretization spacing along each of the parametric coordinates, and mapping what we have in the parent element back to the physical element. The test computations we present for pure-advection cases show that the parameters proposed result in good solution profiles.

Keywords

Space–time computational methods Stabilization parameter Discontinuity-capturing parameter Advection–diffusion equation Incompressible-flow Navier–Stokes equations Isogeometric discretization Finite element discretization 

Notes

Acknowledgements

This work was supported (first and third authors) in part by Grant-in-Aid for Challenging Exploratory Research 16K13779 from JSPS; Grant-in-Aid for Scientific Research (S) 26220002 from the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT); Council for Science, Technology and Innovation (CSTI), Cross-Ministerial Strategic Innovation Promotion Program (SIP), “Innovative Combustion Technology” (Funding agency: JST); and Rice–Waseda research agreement. The computational method parts of the work were also supported (second author) in part by ARO Grant W911NF-17-1-0046 and Top Global University Project of Waseda University.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Kenji Takizawa
    • 1
  • Tayfun E. Tezduyar
    • 2
    • 3
  • Yuto Otoguro
    • 1
  1. 1.Department of Modern Mechanical EngineeringWaseda UniversityTokyoJapan
  2. 2.Mechanical EngineeringRice University – MS 321HoustonUSA
  3. 3.Faculty of Science and EngineeringWaseda UniversityTokyoJapan

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