Higher-order surface FEM for incompressible Navier-Stokes flows on manifolds

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Stationary and instationary Stokes and Navier-Stokes flows are considered on two-dimensional manifolds, ie, on curved surfaces in three dimensions. The higher-order surface FEM is used for the approximation of the geometry, velocities, pressure, and Lagrange multiplier to enforce tangential velocities. Individual element orders are employed for these various fields. Streamline-upwind stabilization is employed for flows at high Reynolds numbers. Applications are presented, which extend classical benchmark test cases from flat domains to general manifolds. Highly accurate solutions are obtained, and higher-order convergence rates are confirmed.

Original languageEnglish
Pages (from-to)55-78
Number of pages24
JournalInternational journal for numerical methods in fluids
Volume88
Issue number2
DOIs
Publication statusPublished - 20 Sep 2018

Fingerprint

Incompressible Navier-Stokes
Stokes Flow
Higher Order
Finite element method
Element Order
Curved Surface
Lagrange multipliers
Streamlines
Navier-Stokes
Stokes
Reynolds number
Three-dimension
Convergence Rate
Stabilization
Benchmark
Geometry
Approximation

Keywords

  • higher-order FEM
  • manifold
  • Navier-Stokes
  • Stokes
  • surface FEM
  • surface PDEs

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Applied Mathematics

Fields of Expertise

  • Human- & Biotechnology

Cite this

Higher-order surface FEM for incompressible Navier-Stokes flows on manifolds. / Fries, Thomas Peter.

In: International journal for numerical methods in fluids, Vol. 88, No. 2, 20.09.2018, p. 55-78.

Research output: Contribution to journalArticleResearchpeer-review

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