Finite-difference solutions of the Navier-Stokes equations for axially symmetric flows in spherical gaps

  • Egon Krause
  • Fritz Bartels
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 771)


Finite-difference solutions of the Navier-Stokes equations are adapted to the calculation of flows in spherical gaps. The equations of motion are restricted to axially symmetric flows so that the stream-function-vorticity formulation can be employed. Thereby the rather difficult calculation of the pressure field is avoided. Only the velocity and vorticity distributions can be determined. Since Taylor-Görtler vortices can be formed in such flows the solution is time dependent and may not reach a steady state, not even for large times. For that reason the truncation errors must be kept sufficiently small and the damping introduced in the discretization cannot exceed certain critical values. Since the solution is almost periodic in the colateral direction, error bounds can be derived for the spatial resolution. The influence of the time-step is analysed with a model equation. The results indicate that for the reasons mentioned the spacing is never arbitrary not even for implicit formulations. Several sample calculations confirm the validity of the error bounds derived.


Flow Mode Angular Acceleration Symmetric Flow Vorticity Component Prescribe Boundary Condition 
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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Egon Krause
    • 1
  • Fritz Bartels
    • 1
  1. 1.Aerodynamisches InstitutRWTH AachenAachenGermany

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