A Vorticity Creation Algorithm for the Navier-Stokes Equations in Arbitrary Domain

  • G.-H. Cottet


We propose an algorithm of vorticity creation type for the Navier-Stokes equation in arbitrary two dimensional domains. This algorithm can be seen as a rephrasing of Chorin’s popular algorithm and one can prove its convergence in the linear case under the sole assumption that the initial enstrophy is finite. The convergence proof follows from delicate energy estimates.


Energy Estimate Linear Case Vorticity Field Vortex Sheet Vortex Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anderson, C. (1989), Vorticity boundary conditions and boundary vorticity generation for two-dimensional viscous incompressible flows, J. Comp. Phys. 80, p. 72–97.ADSCrossRefMATHGoogle Scholar
  2. Beale, J.T. and C. Greengard (1993), Convergence of Euler-Stokes splitting of the Navier-Stokes equations, Comm. Pure Appl. Math. 43.Google Scholar
  3. Benfatto, G. and M. Pulvirenti (1986), Convergence of Chorin-Marsden product formula in the half-plane, Comm. Math. Phys. 106, p. 427–458.MathSciNetADSCrossRefMATHGoogle Scholar
  4. Chorin, A.J. (1973), Numerical study of slightly viscous flow, J. Fluid Mech. 57, p. 785–796.MathSciNetADSCrossRefGoogle Scholar
  5. Chorin, A.J., Hugues, T.J.R. and J.E. Marsden (1978), Product formula and numerical algorithms, Comm. Pure AppL Math. 31, p. 205–256.MathSciNetCrossRefMATHGoogle Scholar
  6. Cottet, G.-H. (1988), Vorticity boundary conditions and the deterministic vortex method for the Navier-Stokes equations in exterior domains, in: Caflish, R. (ed.), Mathematical aspects of vortex dynamics, (SIAM, Philadelhia).Google Scholar
  7. Hou, T. and B. Wetton (1992), Convergence of a finite-difference method for the Navier-Stokes equations using vorticity boundary conditions, SIAM J. Num. Anal. 29, p. 615–639.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • G.-H. Cottet
    • 1
  1. 1.LMC-IMAGUniversité de GrenobleGrenoble CedexFrance

Personalised recommendations