The over-relaxation factor in the numerical solution of the Omega equation
Stuart, David W.
O'Neill, Thomas H.R.
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Results of tests for the optimum over-relaxation coefficients in the numerical relaxation of the omega equation we presented. One case considers a strong upper-level development for tests on a fixed grid using one-, two-, and three-dimensional forms of the omega equation. In the other case of a “classical storm” the omega equation is relaxed in its three-dimensional form using several different horizontal grids. For the one- and two-dimensional tests, the the relaxation scheme aggressively well with theory. In the three-dimensional tests, the observed over-relaxation coefficients are found to be less than the values given by the theory for all grid sizes considered. A sharp cut-off is found to be less than the values given by the theory for all grid sizes considered. A sharp cut-off is found to occur shortly after the optimum over-relaxation value is reached regardless of the number of dimensions of the equation or the size of the grid.
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