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Finite Element Mesh Adjusted to Singularities Applied to Axisymmetric and Plane Flow

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • Pavel Burda

    (Czech Univ. Technology, Department of Mathematics, Faculty of Mechanical Engineering)

  • Jaroslav Novotný

    (Institute of Thermomechanics AS CR)

  • Bedřich Sousedík

    (Czech University of Technology, Department of Mathematics, Faculty of Civil Engineering)

  • Jakub Šístek

    (Czech Univ. Technology, Department of Mathematics, Faculty of Mechanical Engineering)

Abstract

Summary We consider the Navier-Stokes equations for incompressible flow in axisymmetric tubes with abrupt changes of diameter. This paper is based on results for the asymptotics of the solution in the vicinity of nonconvex internal angles where the velocities possess an expansion u(ρ, ϑ) = ρ γ ϕ(ϑ) + …, where ρ, ϑ are local spherical coordinates. Problems with corners, edges, etc. are often successfully solved by the finite element method using an adaptive strategy usually based on a posteriori error estimates. In our paper we suggest an alternative approach for the mesh refinement near the corners, which makes use of the above expansion. It gives very precise results in a cheap way. We give numerical results and show the pros and cons of this approach.

Suggested Citation

  • Pavel Burda & Jaroslav Novotný & Bedřich Sousedík & Jakub Šístek, 2004. "Finite Element Mesh Adjusted to Singularities Applied to Axisymmetric and Plane Flow," Springer Books, in: Miloslav Feistauer & Vít Dolejší & Petr Knobloch & Karel Najzar (ed.), Numerical Mathematics and Advanced Applications, pages 186-195, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18775-9_16
    DOI: 10.1007/978-3-642-18775-9_16
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