The development and testing of characteristic-based semi -Lagrangian two-dimensional shallow water equations model
Abstract
Semi-Lagrangian integration method combined with the method of characteristics is applied to the two-dimensional shallow water equations in the pursuit of development of an alternative stable and accurate numerical integration engine for numerical weather prediction. The newly developed model employs forward trajectory with cubic spline 'internet interpolation' method (Sun et a1. 1996; Sun and Yeh 1997) for semi-Lagrangian treatment and predictor-corrector steps for forcing and source term treatment such as Coriolis force and terrain effect. The model accurately depicts sharp gradient processes and shock propagation that most traditional Eulerian or semi-Lagrangian models fail to simulate or poorly perform. Tested cases are linear and/or nonlinear, 1D and/or 2D problems of triangle, rectangle, Gaussian wave propagation, hydraulic jump, dam break problems, geostrophic adjustment process, symmetric vortex pair merger, shear instability, and vortex-terrain interaction with various mass, momentum initializations. For selected cases, comparison has been made with Eulerian 4th order Runge-Kutta scheme (RK4), forward-backward semi-Lagrangian scheme (FBSL), and analytical solutions. Results indicate that the proposed scheme outperforms both RK4 and FBSL and exhibits satisfactory mass and total energy conservation properties. Analysis of the vortex-terrain interaction cases shows that the model captures the beta-gyre effect well. In particular, when imbalanced mass momentum initialization is used with weak hurricane-like vortex structure for initial momentum, Rossby wave with wavenumber 4 structure around the Gaussian surface terrain is observed. It appears that the shear zone introduced by the initial momentum field acts as an energy source for the disturbance growth, amplified by barotropic instability mechanism. When the topographic beta effect is enhanced, the wave structure becomes more prominent. The proposed scheme delivers overall high accuracy with shock capturing capabilities, showing promising potential for regional climate modeling with high resolution global or limited area atmospheric models.
Degree
Ph.D.
Advisors
Sun, Purdue University.
Subject Area
Atmosphere
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