Semi-Lagrangian, Semi-Implicit Solutions of the Shallow Water Equations in One Dimension.

摘要

The semi-Lagrangian, semi-implicit method is used to model the one dimensional shallow water system of equations with surface topography. The forecasts are compared to finite difference and semi-Lagrangian, explicit forecasts. In the first experiment, a non-rotating system is considered. The semi-Lagrangian, semi-implicit model agrees very well with hydraulic jump theory, while the semi-Lagrangian, explicit model exhibits excessive smoothing and the finite difference model breaks down when the nonlinear interactions become too large. In the second experiment, the system is allowed to rotate to examine the effect of rotation on the formation of topographically induced hydraulic jumps. Although further study is necessary, it is clear that rotation retards the development of the low pressure to the lee of the obstacle. A larger domain and higher spatial resolution are needed for more detailed simulation of hydraulic jumps. Keywords: Meteorology; Numerical weather prediction; Theses; Semi-Lagrangian functions.