Splitting methods for problems with different timescales

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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

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Browning, G. L., & Kreiss, H. O. (1994). Splitting methods for problems with different timescales. Monthly Weather Review, 122(11), 2614–2622. https://doi.org/10.1175/1520-0493(1994)122<2614:SMFPWD>2.0.CO;2

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