A numerical iteration scheme is presented for the calculation of coherent vortex structures. Steady solutions of the Euler vorticity equation are found, using a variational characterization for dipolar and monopolar vortices as relative equilibria of the Poisson system. The variational principle for the vorticity is solved by a numerical method for nonconvex optimization. Besides the variational principle for the vorticity, an optimization process is used for the multipliers that appear in the description. The free boundary is solved implicitly in the iteration process.
SUMMARYThe stationary Reynolds equation is solved over a rectangular region. The problem is linearized by Picard linearization. The ADI method is used to solve the resulting set of linear equations. A set of parameters is introduced to speed up convergence as well for the Picard linearization as for the ADI method. A comparison is made with Booy-Coleman's method. Results are given for bearing numbers 10 to 1000.
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