Abstract
A semi-Lagrangian semi-implicit scheme with additional vertical splitting is developed for nonhydrostatic atmospheric model. The essential elements of the scheme are solution of the trajectory equations for advective part, separation of the vertical normal modes in fast and slow processes with respect to gravity wave propagation speed for each mode, explicit and simpler approximation of slower vertical modes and implicit time differencing for faster modes. This approach allows us to choose the time step based on accuracy considerations and substitute 3D elliptic problems inherent for semi-implicit time differencing by a set of 2D elliptic problems. The performed numerical experiments show computational efficiency of the proposed scheme and accuracy of the predicted atmospheric fields.
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