Completely splitting method for the Navier-Stokes problem

  • I. V. Kireev
  • U. Rüde
  • V. V. Shaidurov
Conference paper
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM) book series (NNFM, volume 88)


We consider two-dimensional time-dependent Navier-Stokes equations in a rectangular domain and study the method of full splitting [3]–[4]. On the physical level, this problem is splitted into two processes: convection-diffusion and action of pressure. The convection-diffusion step is further splitted in two geometric directions. To implement the finite element method, we use the approach with uniform square grids which are staggered relative to one another. This allows the Ladyzhenskaya-Babuška-Brezzi condition for stability of pressure to be fulfilled without usual diminishing the number of degrees of freedom for pressure relative to that for velocities. For pressure we take piecewise constant finite elements. As for velocities, we use piecewise bilinear elements.


Linear Algebraic Equation Multigrid Method Split Method Fractional Step Extended Domain 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • I. V. Kireev
    • 1
  • U. Rüde
    • 2
  • V. V. Shaidurov
    • 1
  1. 1.Institute of Computational Modelling SB RASAcademgorodokKrasnoyarskRussia
  2. 2.University of Erlangen-NurembergErlangenGermany

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