Computations of shallow water equations with high-order central-upwind schemes on triangular meshes

New high-order central-upwind schemes on triangular meshes are proposed to approximate the solutions of shallow water equations. The nonuniform width of the different local Riemann fans is calculated more accurately, and the new central-upwind schemes are of simplicity, universality and robustness. At the same time, due to the central-upwind schemes are combined with new reconstructions based on adaptive least squares, the schemes have the almost non-oscillatory behavior. The numerical results show the desired accuracy, high-resolution, and robustness of our methods.