Two approximation methods of spatial derivatives on unstructured triangular meshes and their application in computing two dimensional flows

Two approximation methods (the Green's theorem technique and the directional derivative technique) of spatial derivatives have been proposed for finite differences on unstructured triangular meshes. Both methods have the first order accuracy. A semi-implicit time matching methods beside the third order Adams-Bashforth method are used in integrating the water shallow equations written in both non-conservative and conservative forms. To remove spurious waves, a smooth procedure has been used. The model is tested on rectangular grids triangulari2jed after the 8-neighbours strategy. In the context of the semi-implicit time matching methods, the directional Derivative technique is more accurate than Green's theorem technique. The results from the third order Adams-Bashforth scheme are the most accurate, especially for discontinuous problems. In this case, there is a minor difference between two approximation techniques of spatial derivatives