Extending the stability range of the composed approximation for free surfaces

The Composed Approximation for finite difference modeling of a solid free s urface has previously been found to have serious stability problems for sig nificant ranges of the physical parameters. Here it is shown that these pro blems can always be avoided by choosing the grid spacings to be unequal in the two directions, with appropriate ratios of the two spacings. The demons tration involves an explicit construction of the main unstable mode, which shows its dependence on the grid-space ratio. This analysis is backed up by numerical tests that show that given an appropriate choice of the spacing ratio-as deduced from the explicit construction-there are no serious stabil ity problems over a full range of the physical parameters. The Composed App roximation in this format gives accurate results for a wide class of physic al situations.