Multi-domain Finite Element — Spectral Chebyshev Parallel Navier-Stokes Solver for Viscous Flow Problems

  • W. Borchers
  • S. Kräutle
  • R. Pasquetti
  • R. Peyret
  • R. Rautmann
Conference paper
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM) book series (NNFM, volume 82)


The paper is concerned with a hybrid finite element — spectral Chebyshev parallel solver of the incompressible Navier-Stokes equations. A domain decomposition, well adapted to the computation of wake or jet type flow, is assumed. Subdomains with complex geometry are handled with finite elements and the other ones with the highly accurate spectral method. The iterative resolution of the multi-domain problem is carried out with the “Conjugate Gradient Boundary Iteration” method. Here we focus on its optimal preconditioning when Gauss-Lobatto type grids are involved. The resulting algorithm is then applied to the flow past a cylinder and over a backward facing step at higher Reynolds numbers. For the latter case the numerical results display some transitional laminar-turbulent behaviour of the flow arising from unstable steady states. Numerical results are presented for both convective and absolute instability regions.


High Reynolds Number Domain Decomposition Strouhal Number Spectral Element Method Projection Step 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • W. Borchers
    • 1
  • S. Kräutle
    • 1
  • R. Pasquetti
    • 2
  • R. Peyret
    • 2
  • R. Rautmann
    • 3
  1. 1.Institut für Angewandte MathematikFriedrich-Alexander Universität Erlangen-NürnbergErlangenGermany
  2. 2.Laboratoire J.A. Dieudonné, UMR CNRS 6621Université de Nice-Sophia AntipolisNiceFrance
  3. 3.Fachbereich Mathematik InformatikUniversität-Gesamthochschule PaderbornGermany

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