Advertisement

Space-Time NURBS-Enhanced Finite Elements for Solving the Compressible Navier–Stokes Equations

  • Michel MakeEmail author
  • Norbert Hosters
  • Marek Behr
  • Stefanie Elgeti
Chapter
  • 95 Downloads
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 132)

Abstract

This article considers the NURBS-Enhanced Finite Element Method (NEFEM) applied to the compressible Navier–Stokes equations. NEFEM, in contrast to conventional finite element formulations, utilizes a NURBS-based computational domain representation. Such representations are typically available from Computer-Aided-Design tools. Within the NEFEM, the NURBS boundary definition is utilized only for elements that are touching the domain boundaries. The remaining interior of the domain is discretized using standard finite elements. Contrary to isogeometric analysis, no volume splines are necessary.

The key technical features of NEFEM will be discussed in detail, followed by a set of numerical examples that are used to compare NEFEM against conventional finite element methods with the focus on compressible flow.

Keywords

Spline-based methods NURBS-enhanced finite elements Stabilized space-time finite elements Compressible Navier–Stokes equations 

References

  1. 1.
    Aliabadi, S.K., Tezduyar, T.E.: Parallel fluid dynamics computations in aerospace applications. Int. J. Numer. Methods Fluids 21(10), 783–805 (1995)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bashkin, V.A., Vaganov, A.V., Egorov, I.V., Ivanov, D.V., Ignatova, G.A.: Comparison of calculated and experimental data on supersonic flow past a circular cylinder. Fluid Dyn. 37(3), 473–483 (2002). https://doi.org/10.1023/A:1019675027402 CrossRefGoogle Scholar
  3. 3.
    Hauke, G., Hughes, T.J.R.: A Comparative study of different sets of variables for solving compressible and incompressible flows. Comput. Methods Appl. Mech. Eng. 153(1–2), 1–44 (1998)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Hosters, N., Helmig, J., Stavrev, A., Behr, M., Elgeti, S.: Fluid–structure interaction With NURBS-based coupling. Comput. Methods Appl. Mech. Eng. 332, 520–539 (2018). https://doi.org/10.1016/j.cma.2018.01.003 MathSciNetCrossRefGoogle Scholar
  5. 5.
    Hughes, T.J.R., Mallet, M.: A new finite element formulation for computational fluid dynamics: IV. Discontinuity-capturing operator for multidimensional advective-diffusive systems. Comput. Methods Appl. Mech. Eng. 58, 329–339 (1986)zbMATHGoogle Scholar
  6. 6.
    Hughes, T.J.R., Cottrell, J.A., Bazilevs, Y.: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Eng. 194, 4135–4195 (2005)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Hughes, T.J.R., Scovazzi, G., Tezduyar, T.E.: Stabilized methods for compressible flows. SIAM J. Sci. Comput. 43(3), 343–368 (2010). https://doi.org/10.1007/s10915-008-9233-5 MathSciNetCrossRefGoogle Scholar
  8. 8.
    Kirk, B.J.: Adaptive Finite Element Simulation of Flow and Transport Applications on Parallel Computers. The University of Texas, Austin (2009)Google Scholar
  9. 9.
    Sevilla, R., Fernández-Méndez, S., Huerta, A.: NURBS-enhanced finite element method (NEFEM). Int. J. Numer. Methods Eng. 76(1), 56–83 (2008)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Stavrev, A., Knechtges, P., Elgeti, S., Huerta, A.: Space-time NURBS-enhanced finite elements for free-surface flows. 2D. Int. J. Num. Methods Fluids 81, 426–450 (2016)CrossRefGoogle Scholar
  11. 11.
    Vassberg, J.C., Jameson, A.: In pursuit of grid convergence for two-dimensional Euler solutions. J. Aircr. 47(4), 1152–1166 (2010). https://doi.org/10.2514/1.46737 CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Michel Make
    • 1
    Email author
  • Norbert Hosters
    • 1
  • Marek Behr
    • 1
  • Stefanie Elgeti
    • 1
  1. 1.RWTH-Aachen UniversityAachenGermany

Personalised recommendations