Comparison of 2D triangular C-grid shallow water models

An ideal two-dimensional (2D) shallow water model should be able to simulate correctly various types of waves including pure gravity and inertia-gravity waves. In this paper, two different triangular C-grid methods are considered, and their dispersion of pure gravity waves, frequencies of inertia-gravity waves and geostrophic balance solutions are investigated. The proposed C-grid methods employ different spatial discretization schemes for coupling shallow water equations together with the various reconstruction techniques for tangential velocity estimation. The proposed reconstruction technique for the second method, which is analogous to a hexagonal C-grid scheme, is shown to be energy conservative and satisfies the geostrophic balance exactly while it supports the unphysical geostrophic modes for hexagonal C-grid. Because of the importance of the application of 2D shallow water models on fully unstructured grids, particular attention is also given to various types of isosceles triangles that may appear in such grids. For the gravity waves, the results of the phase speed ratio of the computed phase speeds over the analytical one are shown and compared. The non-dimensional frequencies of various modes for inertia-gravity waves are also investigated and compared in terms of being monotonic and isotropic respect to the continuous solution. The analyses demonstrate some advantages of the first method in phase speed behaviour for gravity waves and monotonicity of inertia-gravity dispersion. The results of the dispersion analysis are verified through a number of numerical tests. The first method, which is shown to have a better performance, examined through more numerical tests in presence of various source terms and results confirm its capability.