A class of semi-implicit predictor–corrector schemes for the time integration of atmospheric models

In this paper a class of semi-implicit predictor–corrector time integration schemes is proposed. Linear stability analysis is used to identify promising methods and these are applied to the nonlinear system of the shallow water equations on an icosahedral grid. The model used is a testbed for the future development of a more complete atmospheric model. Experiments with standard test cases from the literature show that the investigated time integration schemes produce stable results with relatively long time-steps while maintaining a sufficient level of accuracy. These facts suggest that the analysed methods could be useful for the construction of a more complex model based on the Euler equations.