A Multigrid LGS Method for the Vorticity-Velocity Navier-Stokes Equations

  • M. Napolitano
  • G. Pascazio
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 29)


In the last years robust and efficient numerical schemes have been developed by one of the authors for solving viscous steady flows in two dimensions |1–4|. All of these schemes use the vorticity-stream function Navier-Stokes equations discretized in space by means of central differences to achieve solutions free of numerical viscosity. A clever use of a deferred correction strategy |5|, made possible by the delta form of the equations |6|, combined with a robust multigrid block-line-Gauss-Seidel relaxation procedure, allows to achieve steady solutions to difficult problems at a very reasonable computer cost |7|. A new effort has now been undertaken, aimed at developing a similar approach for three-dimensional flows. The vorticity-vector potential equations |8|, which are the extension to three dimensions of the vorticity-stream function formulation, have been discarded because of the difficulty in the treatment of the boundary conditions. The primitive variable (pressure-velocity) formulation has also been discarded in order to avoid the cumbersome treatment of the correct integral conditions for the pressure |9|. Therefore, the vorticity-velocity equations are being considered.


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Copyright information

© Springer Fachmedien Wiesbaden 1990

Authors and Affiliations

  • M. Napolitano
    • 1
  • G. Pascazio
    • 1
  1. 1.Istituto di Macchine ed EnergeticaUniversità di BariBariItaly

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