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