Abstract: Accuracy and efficiency are two key factors for the numerical simulation of N-S equations in computational fluid dynamics.In this paper,the Eulerian-Lagrangian alternating direction implicit(ELADI)finite difference method for 2D shallow water equations in orthogonal curvilinear coordinate system is extensively discussed together with the basic principle and discretization methods.The ELADI method combines the alternating direction implicit method (ADI)with the Eulerian-Lagrangian Method(ELM).The numerical diffusivity of the ELM method is analyzed.The ELADI method is compared with traditional methods using the laboratory experiments conducted in a curved flume,as well as field measurements from the Haoxue river bend in the upper,lingjiang Reach of the Yangtze River.The result shows that the ELADI method improves computational efficiency greatly with satisfactory accuracy.For the test case, ELADI even allows the Courant number reaching 40 and reducing the computational cost by 90% compared to the traditional method.