THE OVER-RELAXATION FACTOR IN THE NUMERICAL SOLUTION OF THE OMEGA EQUATION

Abstract

Results of tests for the optimum over-relaxation coefficients in the numerical relaxation of the omega equation are 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 relaxation scheme agreesv ery 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 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.