Splitting methods for problems with different timescales

Abstract

Using the mathematical analysis developed in a previous manuscript, it is shown that splitting schemes are not appropriate for badly skewed hyperbolic systems. In a number of atmospheric models, the semi-implicit method is used to treat the badly skewed vertical sound wave terms. This leads to the excitation of the high-frequency waves in a nonphysical manner. It is also shown that this is equivalent to solving the primitive equations; that is, a model using this method for the large-scale case will be ill posed at the lateral boundaries. -from Authors