A modified SOR method for the Poisson equation in unsteady free-surface flow calculations.

Convergence difficulties that sometimes occur if the successive overrelaxation (SOR) method is applied to the Poisson equation on a region with irregular free boundaries are analyzed. It is shown that these difficulties are related to the treatment of the free boundaries and caused by the appearance of complex eigenvalues in the system of discrete equations, when standard centered differences are used. After a modification of this system of equations such that the complex eigenvalues become small, a modified SOR method is presented where two relaxation factors are used alternately. The method leads to fast convergence without requiring specific information about the complex eigenvalues.